Abstract
We study classes of nth 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 +/-infinity 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.
| Original language | English |
|---|---|
| Pages (from-to) | 1-40 |
| Journal | Electronic Journal of Qualitative Theory of Differential Equations |
| Issue number | 28 |
| DOIs | |
| Publication status | Published - 2010 |
Research Keywords
- Nontrivial solutions
- boundary value problems
- nonhomogeneous boundary conditions
- Leray-Schauder degree
- Krein-Rutman theorem
- 2ND-ORDER DIFFERENTIAL-EQUATIONS
- SYMMETRIC POSITIVE SOLUTIONS
- OPTIMAL EXISTENCE CRITERIA
- NONTRIVIAL SOLUTIONS
Publisher's Copyright Statement
- This full text is made available under CC-BY 4.0. https://creativecommons.org/licenses/by/4.0/
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