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NONTRIVIAL SOLUTIONS FOR STURM–LIOUVILLE SYSTEMS VIA A LOCAL MINIMUM THEOREM FOR FUNCTIONALS

Part of: Boundary value problems Equations and inequalities involving nonlinear operators

Published online by Cambridge University Press:  13 June 2013

GABRIELE BONANNO ,
SHAPOUR HEIDARKHANI  and
DONAL O’REGAN
GABRIELE BONANNO
Affiliation:
Department of Civil, Information Technology, Construction, Environmental Engineering and Applied Mathematics, University of Messina, 98166 - Messina, Italy email [email protected]
SHAPOUR HEIDARKHANI*
Affiliation:
Department of Mathematics, Faculty of Sciences, Razi University, 67149 Kermanshah, Iran School of Mathematics, Institute for Research in Fundamental Sciences (IPM), P.O. Box: 19395-5746, Tehran, Iran
DONAL O’REGAN
Affiliation:
School of Mathematics, Statistics and Applied Mathematics, National University of Ireland, Galway, Ireland email [email protected]
*
✉[email protected]
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Abstract

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In this paper, employing a very recent local minimum theorem for differentiable functionals, the existence of at least one nontrivial solution for a class of systems of $n$ second-order Sturm–Liouville equations is established.

Keywords

nontrivial solutionsecond-order Sturm–Liouville systemvariational methodscritical point theory

MSC classification

Secondary: 34B15: Nonlinear boundary value problems 47J10: Nonlinear spectral theory, nonlinear eigenvalue problems
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 89 , Issue 1 , February 2014 , pp. 8 - 18
Copyright
Copyright ©2013 Australian Mathematical Publishing Association Inc. 

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