Existence of Positive Solutions for a Class of Singular Two Point Boundary Value Problems of Second Order Nonliear Equation

Yang Zuodong

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Yang Zuodong. Existence of Positive Solutions for a Class of Singular Two Point Boundary Value Problems of Second Order Nonliear Equation[J]. Applied Mathematics and Mechanics, 1996, 17(5): 445-454.

Citation:

Yang Zuodong. Existence of Positive Solutions for a Class of Singular Two Point Boundary Value Problems of Second Order Nonliear Equation[J]. Applied Mathematics and Mechanics, 1996, 17(5): 445-454.

Citation:

Yang Zuodong. Existence of Positive Solutions for a Class of Singular Two Point Boundary Value Problems of Second Order Nonliear Equation[J]. Applied Mathematics and Mechanics, 1996, 17(5): 445-454.

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Existence of Positive Solutions for a Class of Singular Two Point Boundary Value Problems of Second Order Nonliear Equation

Yang Zuodong

Department of Mathematics, Henan Normal University, Xinxiang Henan 453002, R. P. China

Received Date: 1993-04-15
Rev Recd Date: 1995-04-05
Publish Date: 1996-05-15

Abstract

Abstract

In this paper, we establish the existence of positive solutions of (|y'|^p-2y')'+f(t,y)= 0 (p>1). y(0)=y(1)=0. The function f is allowed to be singular when y=0.
- singular boundary value problems,
- nonlinear,
- positive solution,
- existence

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References(11)

References

[1]	M.A.Herrero and J.L.Vazquez,On the propagation properties of a nonlinear degenerate parabolic equation,Comm.P.D.E.,7 (1982),1381-1402.
[2]	J.R.Esteban and J.L.Vazquez,On the equation of turbulent filtration in one-dimensional porous media,Nonlinear Anal.,10 (1986),1303-1325.
[3]	S.Fucik.J.Necas,J.Soucek and V.Soucek,Spectral Analysis of nonlinear operator,Lecture Notps in Matlt,Springer,Berlin (1973),346.
[4]	Z.M.Guo,Solvability of some singular nonlinear boundary value problems and existence of positive radial solutions of some nonlinear elliptic problems,Nonlinear Anal.,16,9 (1991),781-790.
[5]	姜杰,一类奇异的二阶非线性常微分方程边值问题的正解,吉林大学学报,(1) (1992) ,47-50.
[6]	L.E.Bobisud,D.O'Regan and W.D.Royalty,Solvability of some nonlinear boundary value problems,Nonlinear Anal.,12,9 (1988),855-869.
[7]	D.O'Regan,Positive solutions to singular and non-singular second order boundary value problems,J.Math.Anal.Appl.,142 (1989),40-52.
[8]	J.A.Gatica,Singular nonlinear boundary value problems for second-order ordinary differential equations,J.Diff.Eqs.,79 (1989).62-78.
[9]	D.O'Regan,Existence of positive solutions to some singular and nonsingular second order boundary value problems,J.Diff.Eqs,84 (1990),228-251.
[10]	M.D.Pino,Melgueta and R.Manasevich,A homotopic deformation along p of a Leary-Schauder degree result and existence for (\|y'\|^p-2g')'+f(t,y)=0,u(O)=u(T)=0,p>1.J.Diff.Eqs.,80 (1098),1-13.
[11]	杨作东、柴新宽、郭宗明、王元,一类奇异二阶非线性方程两点边值问题解的存在性和唯一性,《中国力学会第五届现代数学和力学学术会议论文集(MMM-V)》,中国矿业大学出版社(1993),101-105.