Multiple sign-changing solutions for some m-point boundary-value problems. (English) Zbl 1058.34013

Xu, Xian

Electron. J. Differ. Equ. 2004, Paper No. 89, 14 p. (2004).

The purpose of this paper is to give some existence results for multiple sign-changing solution of the m-point boundary value problem \[ y''(t)+f(y)=0,\qquad 0\leq t\leq 1,\quad y(0)=0, \qquad y(1)=\sum_{i=1}^{m-2}\alpha_iy(\eta_i), \] with \(\alpha_i>0,\;i=1,2,\cdots,m-2,\;0<\eta_1<\eta_2<\cdots<\eta_{m-2}<1,\;f\in C(\mathbb{R},\mathbb{R})\). The approach is based on fixed-point index and Leray-Schauder degree methods.

Reviewer: Ruyun Ma (Lanzhou)

MSC:

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

Keywords:

\(m\)-point boundary value problem; sign-changing solution; fixed-point index