Higher order multi-point boundary value problems with sign-changing nonlinearities and nonhomogeneous boundary conditions
We study classes of $n$th order boundary value problems consisting of an equation having a sign-changing nonlinearity $f(t,x)$ together with several different sets of nonhomogeneous multi-point boundary conditions. Criteria are established for the existence of nontrivial solutions, positive solution...
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Published in | Electronic journal of qualitative theory of differential equations Vol. 2010; no. 28; pp. 1 - 40 |
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Main Authors | , , , |
Format | Journal Article |
Language | English |
Published |
University of Szeged
01.01.2010
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Online Access | Get full text |
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Summary: | We study classes of $n$th order boundary value problems consisting of an equation having a sign-changing nonlinearity $f(t,x)$ together with several different sets of nonhomogeneous multi-point boundary conditions. Criteria are established for the existence of nontrivial solutions, positive solutions, and negative solutions of the problems under consideration. Conditions are determined by the behavior of $f(t,x)/x$ near $0$ and $\pm\infty$ when compared to the smallest positive characteristic values of some associated linear integral operators. This work improves and extends a number of recent results in the literature on this topic. The results are illustrated with examples. |
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ISSN: | 1417-3875 1417-3875 |
DOI: | 10.14232/ejqtde.2010.1.28 |