Multiplicity of sign-changing solutions for some four-point boundary value problem. (English) Zbl 1152.34006

Xu, Xian; O’Regan, Donal

Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 69, No. 2, 434-447 (2008).

The authors use Leray-Schauder degree theory and the upper and lower solution method to obtain at least four sign-changing solutions, at least two positive solutions and two negative solutions for the second order four-point boundary value problem:
\[ y''(t)+f(t,y(t),y'(t))=0,\quad 0<t<1, \]
\[ y(0)=\alpha_1 y(\eta_1),\quad y(1)=\alpha_2 y(\eta_2), \]
where \(0\leq\alpha_1, \alpha_2\leq 1\), \(0<\eta_1<\eta_2<1\), \(f\in C([0,1]\times \mathbb{R}^2, \mathbb{R})\).

Reviewer: Minghe Pei (Jilin)

MSC:

34B10	Nonlocal and multipoint boundary value problems for ordinary differential equations
34B15	Nonlinear boundary value problems for ordinary differential equations

Keywords:

four-point boundary value problem; Leray-Schauder degree; strict upper and lower solutions; sign-changing solutions

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