一类奇异二阶非线性方程两点边值问题正解存在性*
Existence of Positive Solutions for a Class of Singular Two Point Boundary Value Problems of Second Order Nonliear Equation
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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.
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Key words:
- singular boundary value problems /
- nonlinear /
- positive solution /
- existence
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[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.
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