Bulletin of the Australian Mathematical Society

Research Article

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

GABRIELE BONANNOa1, SHAPOUR HEIDARKHANIa2a3 c1 and DONAL O’REGANa4

a1 Department of Civil, Information Technology, Construction, Environmental Engineering and Applied Mathematics, University of Messina, 98166 - Messina, Italy email bonanno@unime.it

a2 Department of Mathematics, Faculty of Sciences, Razi University, 67149 Kermanshah, Iran

a3 School of Mathematics, Institute for Research in Fundamental Sciences (IPM), P.O. Box: 19395-5746, Tehran, Iran

a4 School of Mathematics, Statistics and Applied Mathematics, National University of Ireland, Galway, Ireland email donal.oregan@nuigalway.ie

Abstract

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 second-order Sturm–Liouville equations is established.

(Received October 04 2012)

(Accepted February 21 2013)

(Online publication June 13 2013)

2010 Mathematics subject classification

  • primary 34B15;
  • secondary 47J10

Keywords and phrases

  • nontrivial solution;
  • second-order Sturm–Liouville system;
  • variational methods;
  • critical point theory

Footnotes

  Research of Shapour Heidarkhani was in part supported by a grant from IPM (No. 91470046).