Remarks on nonlocal boundary value problems at resonance

We show that it is important to allow the nonlinear term to change sign when discussing existence of a positive solution for multipoint, or more general nonlocal, boundary value problems in the resonant case. When the nonlinear term has a fixed sign we obtain simple necessary and sufficient conditio...

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Bibliographic Details
Published in:Applied mathematics and computation 2010-03, Vol.216 (2), p.497-500
Main Author: Webb, J.R.L.
Format: Article
Language:English
Subjects:
Boundary value problems
Computation
Exact sciences and technology
Mathematical analysis
Mathematical models
Mathematics
Nonlinearity
Nonlocal boundary conditions
Numerical analysis
Numerical analysis. Scientific computation
Partial differential equations
Partial differential equations, boundary value problems
Positive solution
Resonance
Sciences and techniques of general use
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Summary:We show that it is important to allow the nonlinear term to change sign when discussing existence of a positive solution for multipoint, or more general nonlocal, boundary value problems in the resonant case. When the nonlinear term has a fixed sign we obtain simple necessary and sufficient conditions for the existence of positive solutions.
ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2010.01.056