Acta mathematica scientia,Series A ›› 2010, Vol. 30 ›› Issue (6): 1503-1513.

• Articles • Previous Articles     Next Articles

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

1LUAN Shi-Xia, 2WAN Fei-Fei, 3ZHANG Xin-Guang   

  1. 1.School of Mathematical Sciences, Qufu Normal University, Shandong Qufu 273165|2.College of Science, Yantai Nanshan College, Shandong Yantai 265713|3.Department of Mathematics and Informational Sciences, Yantai University, Shandong Yantai 264005
  • Received:2008-12-08 Revised:2009-12-14 Online:2010-12-25 Published:2010-12-25
  • Supported by:

    国家自然科学基金(10771117)和山东省青年自然科学基金(Q2007A02, ZR2009AL016)资助

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 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
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