Positive Solutions of Nonlinear Neumann Boundary Value Problems With Sign-Changing Green's Function
2
조회
0
다운로드
0
인용
0
참고문헌
키워드
초록
This paper is concerned with the existence of positive solutions of the nonlin-ear Neumann boundary value problems(u00 + a(t)u = b(t)f(u); t ∈ (0; 1);u0(0) = u0(1) = 0;where a; b ∈ C[0; 1] with a(t) > 0; b(t) 0 and the Green's function of the linear problem(u00 + a(t)u = 0; t ∈(0; 1);u0(0) = u0(1) = 0 may change its sign on [0; 1] [0; 1]. Our analysis relies on the Leray-Schauder fixed point theorem.
Abstract
This paper is concerned with the existence of positive solutions of the nonlin-ear Neumann boundary value problems(u00 + a(t)u = b(t)f(u); t ∈ (0; 1);u0(0) = u0(1) = 0;where a; b ∈ C[0; 1] with a(t) > 0; b(t) 0 and the Green's function of the linear problem(u00 + a(t)u = 0; t ∈(0; 1);u0(0) = u0(1) = 0 may change its sign on [0; 1] [0; 1]. Our analysis relies on the Leray-Schauder fixed point theorem.
참고문헌 (12)
- A. Boscaggin, "A note on a superlinear indefinite Neumann problem with multiple positive solutions", J. Math. Anal. Appl, 377, pp.259~268 (2011)
- J. Chu, "Positive solutions of Neumann problems with singular-ities", J. Math. Anal. Appl, 337, pp.1267~1272 (2008)
- K. Deimling, "Nonlinear functional analysis" (1985), Springer-Verlag
- J. R. Graef, "A periodic boundary value problem with vanishing Green's function", Appl. Math. Lett, 21(2), pp.176~180 (2008)
- D. D. Hai, "Positive solutions to a class of elliptic boundary value problems", J. Math. Anal. Appl, 227, pp.195~199 (1998)
- D. Jiang, "The monotone method for Neumann functional differential equations with upper and lower solutions in the reverse order", Nonlinear. Anal, 67, pp.2815~2828 (2007)
- M. Krasnosel'skii, "Positive solutions of operator equations" (1964), Noordhoff
- Z. Li, "Existence of positive solutions of superlinear second-order Neumann boundary value problem", Nonlinear Anal, 72, pp.3216~3221 (2010)
- R. Ma, "Nonlinear periodic boundary value problems with sign-changing Green's func-tion", Nonlinear Anal, 74, pp.1714~1720 (2011)
- Y. Sun, "Positive solutions for singular second order Neu-mann boundary value problems via a cone fixed point theorem", Appl. Math. Comput, 210, pp.80~86 (2009)
- J. Sun, "Multiple positive solutions to second-order Neumann boundary value problems", Appl. Math. Comput, 146, pp.187~194 (2003)
- J. Sun, "Three positive solutions for second-order Neumann boundary value problems", Appl. Math. Lett, 17, pp.1079~1084 (2004)