具有变号非线性项的多点边值问题的非平凡解

Abstract

Abstract:

In this paper, the authors consider a class of m-point boundary value problems with changing sign nonlinearity

$\left\{\begin{array}{l} (p(t)u'(t))'-q(t)u(t)+ h(t)f(t,u(t))=0,\quad 0<t<1, \disp au(0)-bp(0)u'(0)=\sum_{i=1}^{m-2}\alpha_{i}u(\xi_{i}),\\[3mm]\disp cu(1)+dp(1)u'(1)=\sum_{i=1}^{m-2}\beta_{i}u(\xi_{i}), \end{array}\right.$
where f ∈ C([0,1]×(-∞,+∞),(-∞,+∞)) is a sign-changing function, not necessarily nonnegative and bounded from below. By establishing a more general Leray-Schauder degree theory, and computing the topological degree of a completely continuous field, some existence results of nontrival solutions are obtained.

Key words: Nontrivial solutions, m-point boundary value problems, Singular, Leray-Schauder degree

CLC Number:

34B15| 34B25

LUAN Shi-Xia, WAN Fei-Fei, ZHANG Xin-Guang. Nontrivial Solutions of Multi-point Boundary Value Problems with Sign-changing Nonlinear Terms[J].Acta mathematica scientia,Series A, 2010, 30(6): 1503-1513.

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Nontrivial Solutions of Multi-point Boundary Value Problems with Sign-changing Nonlinear Terms

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