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