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Existence of nontrivial solutions to systems of multi-point boundary value problems

Pages: 273 - 281, Issue special, November 2013

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John R. Graef - Department of Mathematics, University of Tennessee at Chattanooga, Chattanooga, TN 37403, United States (email)
Shapour Heidarkhani - Department of Mathematics, Faculty of Sciences, Razi University, Kermanshah 67149, Iran (email)
Lingju Kong - Department of Mathematics, University of Tennessee at Chattanooga, Chattanooga, TN 37403, United States (email)

Abstract: In this paper, sufficient conditions are established for the existence of at least one nontrivial solution of the multi-point boundary value system $$ \left\{\begin{array}{ll} -(\phi_{p_i}(u'_{i}))'=\lambda F_{u_{i}}(x,u_{1},\ldots,u_{n}),\ x\in(0,1),\\ u_{i}(0)=\sum_{j=1}^m a_ju_i(x_j),\ u_{i}(1)=\sum_{j=1}^m b_ju_i(x_j), \end{array} \right. i=1,\ldots,n. $$ The approach is based on variational methods and critical point theory.

Keywords:  Multi-point boundary value problem, critical point theory.
Mathematics Subject Classification:  Primary: 34B10, 34B15.

Received: July 2012;      Revised: December 2012;      Published: November 2013.

 References