Positive Solutions of Nonlinear Neumann Boundary Value Problems with Sign-Changing Green's Function

다국어 초록 (Multilingual Abstract)

This paper is concerned with the existence of positive solutions of the nonlinear Neumann boundary value problems $$\{u^{{\prime}{\prime}}+a(t)u={\lambda}b(t)f(u),\;t{\in}(0,1),\\u^{\prime}(0)=u^{\prime}(1)=0$$, where $a,b{\in}C[0,1]$ with $a(t)>0,\;b(t){\geq}0$ and the Green's function of the linear problem $$\{u^{{\prime}{\prime}}+a(t)u=0,\;t{\in}(0,1),\\u^{\prime}(0)=u^{\prime}(1)=0$$ may change its sign on $[0,1]{\times}[0,1]$. Our analysis relies on the Leray-Schauder fixed point theorem.

참고문헌 (Reference)

1 J. Sun, "Three positive solutions for second-order Neumann boundary value problems" 17 : 1079-1084, 2004

2 D. Jiang, "The monotone method for Neumann functional differential equations with upper and lower solutions in the reverse order" 67 : 2815-2828, 2007

3 D. D. Hai, "Positive solutions to a class of elliptic boundary value problems" 227 : 195-199, 1998

4 M. Krasnosel'skii, "Positive solutions of operator equations" Noordhoff 1964

5 J. Chu, "Positive solutions of Neumann problems with singular-ities" 337 : 1267-1272, 2008

6 Y. Sun, "Positive solutions for singular second order Neu-mann boundary value problems via a cone fixed point theorem" 210 : 80-86, 2009

7 R. Ma, "Nonlinear periodic boundary value problems with sign-changing Green's func-tion" 74 : 1714-1720, 2011

8 K. Deimling, "Nonlinear functional analysis" Springer-Verlag 1985

9 J. Sun, "Multiple positive solutions to second-order Neumann boundary value problems" 146 : 187-194, 2003

10 Z. Li, "Existence of positive solutions of superlinear second-order Neumann boundary value problem" 72 : 3216-3221, 2010

11 J. R. Graef, "A periodic boundary value problem with vanishing Green's function" 21 (21): 176-180, 2008

12 A. Boscaggin, "A note on a superlinear indefinite Neumann problem with multiple positive solutions" 377 : 259-268, 2011