In this paper, the author obtains an existence theorem of minimal and maximal solutions for the periodic boundary value problems of nonlinear impulsive integrodifferential equations of mixed type in Banach space by me...In this paper, the author obtains an existence theorem of minimal and maximal solutions for the periodic boundary value problems of nonlinear impulsive integrodifferential equations of mixed type in Banach space by means of the monotone iterative technique and cone theory based on a comparison result.展开更多
In this paper, we consider the existence of three nontrivial solutions for a discrete non-linear multiparameter periodic problem involving the p-Laplacian. By using the similar method for the Dirichlet boundary value ...In this paper, we consider the existence of three nontrivial solutions for a discrete non-linear multiparameter periodic problem involving the p-Laplacian. By using the similar method for the Dirichlet boundary value problems in [C. Bonanno and P. Candito, Appl. Anal., 88（4） （2009）, pp. 605-616], we construct two new strong maximum principles and obtain that the boundary value problem has three positive solutions for λ and μ in some suitable intervals. The approaches we use are the critical point theory.展开更多
The periodic boundary value problems for nonlinear functional differential equa- tions was discussed.The existence of maximal and minimal solutions was obtained when the lower and upper solutions satisfied the formal ...The periodic boundary value problems for nonlinear functional differential equa- tions was discussed.The existence of maximal and minimal solutions was obtained when the lower and upper solutions satisfied the formal or reverse order.展开更多
In this paper, we show that the method of monotone iterative technique is valid to obtain two monotone sequences that converge uniformly to extremal solutions to second order periodic boundary value problems and perio...In this paper, we show that the method of monotone iterative technique is valid to obtain two monotone sequences that converge uniformly to extremal solutions to second order periodic boundary value problems and periodic solutions of functional difference equations. We obtain some new results under the lower solution α and upper solutionβ with α≤β展开更多
This paper investigates the maximal and minimal solutions of periodic boundary value problems for second order integro-differential equations in Banach spaces by establishing a comparison result and using the monotone...This paper investigates the maximal and minimal solutions of periodic boundary value problems for second order integro-differential equations in Banach spaces by establishing a comparison result and using the monotone iterative method.展开更多
By establishing a comparison result and using monotone iterative methods, the theorem of existence for minimal and maximal solutions of periodic boundary value problems for second-order nonlinear integro-differential ...By establishing a comparison result and using monotone iterative methods, the theorem of existence for minimal and maximal solutions of periodic boundary value problems for second-order nonlinear integro-differential equations in Banach spaces is proved.展开更多
In this paper, we consider the existence of positive solutions of second-order periodic boundary value problem where 0 〈 ε 〈 1/2, g ： [0, 2π] →R is continuous, f ： [0, ∞） →R is continuous and λ 〉 0 is a pa...In this paper, we consider the existence of positive solutions of second-order periodic boundary value problem where 0 〈 ε 〈 1/2, g ： [0, 2π] →R is continuous, f ： [0, ∞） →R is continuous and λ 〉 0 is a parameter.展开更多
This paper investigates the existence of solutions of periodic boundary value problems for nonlinear second order functional differential equations. By establishing comparison results, criteria on the existence of max...This paper investigates the existence of solutions of periodic boundary value problems for nonlinear second order functional differential equations. By establishing comparison results, criteria on the existence of maximal and minimal solutions are obtained.展开更多
This paper is devoted to the study ofthe existence of single and multiple positive solutions for the first order boundary value problem x′= f（t, x）, x（0） = x（T）, where f ∈ C（[0,T] × R） . In addition, we...This paper is devoted to the study ofthe existence of single and multiple positive solutions for the first order boundary value problem x′= f（t, x）, x（0） = x（T）, where f ∈ C（[0,T] × R） . In addition, we apply our existence theorems to a class of nonlinear periodic boundary value problems with a singularity at the origin. Our proofs are based on a fixed point theorem in cones. Our results improve some recent results in the literatures.展开更多
This paper investigates periodic boundary value problem for first order nonlinear impulsive integro-differelltial equations of mixed type in a Banach space. By establishing a comparison result, criteria on the existen...This paper investigates periodic boundary value problem for first order nonlinear impulsive integro-differelltial equations of mixed type in a Banach space. By establishing a comparison result, criteria on the existence of maximal and minimal solutions are obtained.展开更多
In this paper, the monotone iterative method of Lakshmikantham and a comparison result are applied to study a periodic boundary value problem for a nonlinear impulsive differential equation with 'supremum' and...In this paper, the monotone iterative method of Lakshmikantham and a comparison result are applied to study a periodic boundary value problem for a nonlinear impulsive differential equation with 'supremum' and the existence of maximal and minimal solutions are obtained.展开更多
In this paper, we investigate the problem of the existence of positive solutions to a non-linear second-order periodic boundary value problem. The proof relies on a non-linear alternative of Leray-Schauder type and a ...In this paper, we investigate the problem of the existence of positive solutions to a non-linear second-order periodic boundary value problem. The proof relies on a non-linear alternative of Leray-Schauder type and a fxed point theorem in cones.展开更多
This paper is concerned with the existence and approximation of solutions for a class of first order impulsive functional differential equations with periodic boundary value conditions. A new comparison result is pres...This paper is concerned with the existence and approximation of solutions for a class of first order impulsive functional differential equations with periodic boundary value conditions. A new comparison result is presented and the previous results are extended.展开更多
Aim To investigate the periodic boundary value problem for functional differential equations with impulses. Methods The method of upper and lower solutions and the monotone iterative technique were used to establish...Aim To investigate the periodic boundary value problem for functional differential equations with impulses. Methods The method of upper and lower solutions and the monotone iterative technique were used to establish our results. Results and Conclusion The results of the existence of maximal and minimal solutions of the periodic boundary value problem for functional differential equations with impulses are obtained.展开更多
In this paper, the properties of solution of periodic boundary value problem for second-order impulsive integro-differential equation are discussed. Using the iterative analysis method, the existence and uniqueness of...In this paper, the properties of solution of periodic boundary value problem for second-order impulsive integro-differential equation are discussed. Using the iterative analysis method, the existence and uniqueness of periodic solution and the sufficient condition for uniform stability of trivial solution are obtained, which extend the previous results on integro-differential equation in periodic boundary value problem.展开更多
This paper studies the positive solutions of the nonlinear second-order periodic boundary value problem u″（t） ＋ λ（t）u（t） = f（t,u（t））,a.e.t ∈ [0,2π],u（0） = u（2π）,u′（0） = u′（2π）,where f（t,u）...This paper studies the positive solutions of the nonlinear second-order periodic boundary value problem u″（t） ＋ λ（t）u（t） = f（t,u（t））,a.e.t ∈ [0,2π],u（0） = u（2π）,u′（0） = u′（2π）,where f（t,u） is a local Carath′eodory function.This shows that the problem is singular with respect to both the time variable t and space variable u.By applying the Leggett-Williams and Krasnosel＇skii fixed point theorems on cones,an existence theorem of triple positive solutions is established.In order to use these theorems,the exact a priori estimations for the bound of solution are given,and some proper height functions are introduced by the estimations.展开更多
This paper deals with the existence and multiplicity of positive solutions to second order period boundary value problems with impulse effects. The proof of our main results relies on a well-known fixed point theorem ...This paper deals with the existence and multiplicity of positive solutions to second order period boundary value problems with impulse effects. The proof of our main results relies on a well-known fixed point theorem in cones. The paper extends some previous results and reports some new results about impulsive differential equations.展开更多
This paper uses the method of upper and lower solutions and the monotone iterative technique to investigate the existence of maximal and minimal solutions of the periodic boundary value problem for first order impulsi...This paper uses the method of upper and lower solutions and the monotone iterative technique to investigate the existence of maximal and minimal solutions of the periodic boundary value problem for first order impulsive functional differential equations.展开更多
In this paper the homogenization method is improved to develop one kind of dual coupled approximate method, which reflects both the macro-scope properties of whole structure and its loadings, and micro-scope configura...In this paper the homogenization method is improved to develop one kind of dual coupled approximate method, which reflects both the macro-scope properties of whole structure and its loadings, and micro-scope configuration properties of composite materials. The boundary value problem of woven membrane is considered, the dual asymptotic expression of the exact solution is given, and its approximation and error estimation are discussed. Finally the numerical example shows the effectiveness of this dual coupled method.展开更多
In this paper, by means of iterative analysis, the existence for periodic boundary value problem of first-order integro-differential differential equations are considered. Some new results are obtained.
文摘In this paper, the author obtains an existence theorem of minimal and maximal solutions for the periodic boundary value problems of nonlinear impulsive integrodifferential equations of mixed type in Banach space by means of the monotone iterative technique and cone theory based on a comparison result.
基金Supported by NSFC(11326127,11101335)NWNULKQN-11-23the Fundamental Research Funds for the Gansu Universities
文摘In this paper, we consider the existence of three nontrivial solutions for a discrete non-linear multiparameter periodic problem involving the p-Laplacian. By using the similar method for the Dirichlet boundary value problems in [C. Bonanno and P. Candito, Appl. Anal., 88（4） （2009）, pp. 605-616], we construct two new strong maximum principles and obtain that the boundary value problem has three positive solutions for λ and μ in some suitable intervals. The approaches we use are the critical point theory.
基金Supported by the Education Department Foundation of Shandong Province(J07WH01)
文摘The periodic boundary value problems for nonlinear functional differential equa- tions was discussed.The existence of maximal and minimal solutions was obtained when the lower and upper solutions satisfied the formal or reverse order.
文摘In this paper, we show that the method of monotone iterative technique is valid to obtain two monotone sequences that converge uniformly to extremal solutions to second order periodic boundary value problems and periodic solutions of functional difference equations. We obtain some new results under the lower solution α and upper solutionβ with α≤β
基金Supported by Natural Science Foundation of Hainan Province(10102)
文摘This paper investigates the maximal and minimal solutions of periodic boundary value problems for second order integro-differential equations in Banach spaces by establishing a comparison result and using the monotone iterative method.
基金theNaturalScienceFoundationofEducationalCommitteeofHainanProvince China
文摘By establishing a comparison result and using monotone iterative methods, the theorem of existence for minimal and maximal solutions of periodic boundary value problems for second-order nonlinear integro-differential equations in Banach spaces is proved.
基金Supported by the National Natural Science Foundation of China(No.11321627,11401479,71561024,11561063)China Postdoctoral Science Foundation(2014M562472)+1 种基金Postdoctoral Science Foundation of Gansu Provincethe Science Research Project for Colleges and Universities of Gansu Province(2016A-003)
文摘In this paper, we consider the existence of positive solutions of second-order periodic boundary value problem where 0 〈 ε 〈 1/2, g ： [0, 2π] →R is continuous, f ： [0, ∞） →R is continuous and λ 〉 0 is a parameter.
基金Supported by NNSF-China (No.10071043)the YNSF of Shandong Province (No.Y2000A06)
文摘This paper investigates the existence of solutions of periodic boundary value problems for nonlinear second order functional differential equations. By establishing comparison results, criteria on the existence of maximal and minimal solutions are obtained.
基金Science Foundation for Young Teachers of Northeast Normal University(No:20060108)the National Natural Science Foundation of China(No.10571021)Key Laboratory for Applied Statistics of MOE(KLAS)
文摘This paper is devoted to the study ofthe existence of single and multiple positive solutions for the first order boundary value problem x′= f（t, x）, x（0） = x（T）, where f ∈ C（[0,T] × R） . In addition, we apply our existence theorems to a class of nonlinear periodic boundary value problems with a singularity at the origin. Our proofs are based on a fixed point theorem in cones. Our results improve some recent results in the literatures.
文摘This paper investigates periodic boundary value problem for first order nonlinear impulsive integro-differelltial equations of mixed type in a Banach space. By establishing a comparison result, criteria on the existence of maximal and minimal solutions are obtained.
基金Research supported by the foundation of Educational Department of Fujian Province (K200ll04)and Zhangzhou Teachers College.
文摘In this paper, the monotone iterative method of Lakshmikantham and a comparison result are applied to study a periodic boundary value problem for a nonlinear impulsive differential equation with 'supremum' and the existence of maximal and minimal solutions are obtained.
文摘In this paper, we investigate the problem of the existence of positive solutions to a non-linear second-order periodic boundary value problem. The proof relies on a non-linear alternative of Leray-Schauder type and a fxed point theorem in cones.
基金Supported by the National Natural Science Foundation of China (10571050 10871062)Hunan Provincial Innovation Foundation For Postgraduate
文摘This paper is concerned with the existence and approximation of solutions for a class of first order impulsive functional differential equations with periodic boundary value conditions. A new comparison result is presented and the previous results are extended.
文摘Aim To investigate the periodic boundary value problem for functional differential equations with impulses. Methods The method of upper and lower solutions and the monotone iterative technique were used to establish our results. Results and Conclusion The results of the existence of maximal and minimal solutions of the periodic boundary value problem for functional differential equations with impulses are obtained.
基金Supported by the Natural Science Foundation of Hainan Province（112006） Supported by the Natural Science Foundation of Department of Education of Hainan Province（Hjkj2013-47） Supported by the National Basic Research Program of China（973Program, 2011CB710600）
文摘In this paper, the properties of solution of periodic boundary value problem for second-order impulsive integro-differential equation are discussed. Using the iterative analysis method, the existence and uniqueness of periodic solution and the sufficient condition for uniform stability of trivial solution are obtained, which extend the previous results on integro-differential equation in periodic boundary value problem.
基金Supported by National Natural Science Foundation of China(Grant No.11071109)
文摘This paper studies the positive solutions of the nonlinear second-order periodic boundary value problem u″（t） ＋ λ（t）u（t） = f（t,u（t））,a.e.t ∈ [0,2π],u（0） = u（2π）,u′（0） = u′（2π）,where f（t,u） is a local Carath′eodory function.This shows that the problem is singular with respect to both the time variable t and space variable u.By applying the Leggett-Williams and Krasnosel＇skii fixed point theorems on cones,an existence theorem of triple positive solutions is established.In order to use these theorems,the exact a priori estimations for the bound of solution are given,and some proper height functions are introduced by the estimations.
基金Supported by the National Natural Science Foundation of China(No.10571021,10701020)Key Laboratory for Applied Statistics of MOE(KLAS)
文摘This paper deals with the existence and multiplicity of positive solutions to second order period boundary value problems with impulse effects. The proof of our main results relies on a well-known fixed point theorem in cones. The paper extends some previous results and reports some new results about impulsive differential equations.
文摘This paper uses the method of upper and lower solutions and the monotone iterative technique to investigate the existence of maximal and minimal solutions of the periodic boundary value problem for first order impulsive functional differential equations.
文摘In this paper the homogenization method is improved to develop one kind of dual coupled approximate method, which reflects both the macro-scope properties of whole structure and its loadings, and micro-scope configuration properties of composite materials. The boundary value problem of woven membrane is considered, the dual asymptotic expression of the exact solution is given, and its approximation and error estimation are discussed. Finally the numerical example shows the effectiveness of this dual coupled method.
基金National Natural Science Foundation of China (No.50579089)Natural Science Foundation of Hubei Provincial Department of Education (No.B200704001)+1 种基金Science Foundation for Young of China University of Geosciences (No.CUGQNL0615)Science Foundation for Graduate of China University of Geosciences (No.CUGYJS0709)
文摘In this paper, by means of iterative analysis, the existence for periodic boundary value problem of first-order integro-differential differential equations are considered. Some new results are obtained.
