In this paper the existence of solutions of the singularly perturbed boundary value problems on infinite interval for the second order nonlinear equation containing a small parameterε>0,εy'=f(x,y,y'),y...In this paper the existence of solutions of the singularly perturbed boundary value problems on infinite interval for the second order nonlinear equation containing a small parameterε>0,εy'=f(x,y,y'),y'(0)=a,y(∞)=βis examined,where are constants,and i=0,1.Moreover,asymptotic estimates of the solutions for the above problems are given.展开更多
In this paper, we study the weighted (0,2;0)-interpolation on infinite interval, which means to determine a polynomial of degree ≤3n-1 when the function values are prescribed at two sets of points namely the zeros of...In this paper, we study the weighted (0,2;0)-interpolation on infinite interval, which means to determine a polynomial of degree ≤3n-1 when the function values are prescribed at two sets of points namely the zeros of H n(x) and H ′ n(x) and the wieghted second derivative at the zeros of H n(x).展开更多
In this paper some new results for general orthogonal polynomials on infinite intervals are presented. In particular, an answer to Problem 54 of P. Turan[J. Approximation Theory, 29(1980),P.64] is given.
A new upper and lower solution theory is presented for the second order problem （G＇（y））＇＋ f（t, y） = 0 on finite and infinite intervals. The theory on finite intervals is based on a Leray-Schauder alternative,...A new upper and lower solution theory is presented for the second order problem （G＇（y））＇＋ f（t, y） = 0 on finite and infinite intervals. The theory on finite intervals is based on a Leray-Schauder alternative, where as the theory on infinite intervals is based on results on the finite interval and a diagonalization process.展开更多
This article solved the asymptotic solution of a singularly perturbed boundary value problem with second order turning point, encountered in the dissipative equilibrium vector field of the coupled convection disturban...This article solved the asymptotic solution of a singularly perturbed boundary value problem with second order turning point, encountered in the dissipative equilibrium vector field of the coupled convection disturbance kinetic equations under the constrained filed and the gravity. Using the matching of asymptotic expansions, the formal asymptotic solution is constructed. By using the theory of differential inequality the uniform validity of the asymptotic expansion for the solution is proved.展开更多
This paper considers the solvability of boundary value problems with a p-Laplacian {(φ(u^((n-1))(t)))'=q(t)f(t,u(t),…,u^((n-1))(t)),0<t<+∞,u^((i))(0)=Ai,i=0,1,…,n-3,u^((n-2))(0)-au^((n-1))(0)=B,u^((n-1)...This paper considers the solvability of boundary value problems with a p-Laplacian {(φ(u^((n-1))(t)))'=q(t)f(t,u(t),…,u^((n-1))(t)),0<t<+∞,u^((i))(0)=Ai,i=0,1,…,n-3,u^((n-2))(0)-au^((n-1))(0)=B,u^((n-1))(+∞)=C.By using the methods of upper and lower solution, the schauder fixed point theorem, and the degree theory, we obtain the existence of one and triple solutions. This paper generalizes several problems due to the dependence on the p-Laplacian operator, the n-1-th derivative not only in the differential equation but also in the boundary conditions. The most interesting point is that the solutions may be unbounded.展开更多
Dirichlet boundary value problems for perturbed second-order differential equations on a half line are investigated in this paper. The methods mainly depend on the calculus of variations to the classical functionals. ...Dirichlet boundary value problems for perturbed second-order differential equations on a half line are investigated in this paper. The methods mainly depend on the calculus of variations to the classical functionals. Sufficient conditions are obtained for the existence of the solutions.展开更多
文摘In this paper the existence of solutions of the singularly perturbed boundary value problems on infinite interval for the second order nonlinear equation containing a small parameterε>0,εy'=f(x,y,y'),y'(0)=a,y(∞)=βis examined,where are constants,and i=0,1.Moreover,asymptotic estimates of the solutions for the above problems are given.
文摘In this paper, we study the weighted (0,2;0)-interpolation on infinite interval, which means to determine a polynomial of degree ≤3n-1 when the function values are prescribed at two sets of points namely the zeros of H n(x) and H ′ n(x) and the wieghted second derivative at the zeros of H n(x).
基金The Project Supported by National Natural Science Foundation of China
文摘In this paper some new results for general orthogonal polynomials on infinite intervals are presented. In particular, an answer to Problem 54 of P. Turan[J. Approximation Theory, 29(1980),P.64] is given.
基金Supported by Grant No.201/01/1451 of the Grant Agency of Czech Republicthe Council of Czech Government J14/98:153100011
文摘A new upper and lower solution theory is presented for the second order problem （G＇（y））＇＋ f（t, y） = 0 on finite and infinite intervals. The theory on finite intervals is based on a Leray-Schauder alternative, where as the theory on infinite intervals is based on results on the finite interval and a diagonalization process.
基金Supported by the National Natural Science Foundation of China (No. 11071075, 11171113)the NNFC-the Knowledge Innovation Program of Chinese Academy of Science (No. 30921064, 90820307)E-Institutes of Shanghai Municipal Education Commission (No. E03004)
文摘This article solved the asymptotic solution of a singularly perturbed boundary value problem with second order turning point, encountered in the dissipative equilibrium vector field of the coupled convection disturbance kinetic equations under the constrained filed and the gravity. Using the matching of asymptotic expansions, the formal asymptotic solution is constructed. By using the theory of differential inequality the uniform validity of the asymptotic expansion for the solution is proved.
基金This research was supported by the National Natural Science Foundation of China(No.11601493)by the Fundamental Research Funds for the Central Universities.
文摘This paper considers the solvability of boundary value problems with a p-Laplacian {(φ(u^((n-1))(t)))'=q(t)f(t,u(t),…,u^((n-1))(t)),0<t<+∞,u^((i))(0)=Ai,i=0,1,…,n-3,u^((n-2))(0)-au^((n-1))(0)=B,u^((n-1))(+∞)=C.By using the methods of upper and lower solution, the schauder fixed point theorem, and the degree theory, we obtain the existence of one and triple solutions. This paper generalizes several problems due to the dependence on the p-Laplacian operator, the n-1-th derivative not only in the differential equation but also in the boundary conditions. The most interesting point is that the solutions may be unbounded.
基金Supported by NNSF of China (10371006) and SRFDP(20050007011).
文摘Dirichlet boundary value problems for perturbed second-order differential equations on a half line are investigated in this paper. The methods mainly depend on the calculus of variations to the classical functionals. Sufficient conditions are obtained for the existence of the solutions.
