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On the existence of multiple solutions of the boundary value problem for nonlinear second-order differential equations. (English) Zbl 1046.34038

This article focuses on the following boundary value problem \[ u''+a(x)f(u)=0,\;0<x<1,\quad u(0)=u(1)=0. \] By discussing the relation between the corresponding eigenvalue and the ratio \(\frac{f(s)}{s}\) at infinity and zero, the authors establish some precise results on the sign changing solutions with prescribed nodal properties. The approach is mainly based on the shooting method together with Sturm’s comparison theorem.
Reviewer: Ruyun Ma (Lanzhou)

MSC:

34B15 Nonlinear boundary value problems for ordinary differential equations
35J65 Nonlinear boundary value problems for linear elliptic equations
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