Opuscula Math. 33, no. 2 (2013), 293-306

Opuscula Mathematica

Multiple solutions for systems of multi-point boundary value problems

John R. Graef
Shapour Heidarkhani
Lingju Kong

Abstract. In this paper, we establish the existence of at least three solutions of the multi-point boundary value system \[\left\{\begin{array}{ll} -(\phi_{p_i}(u'_{i}))'=\lambda F_{u_{i}}(x,u_{1},\ldots,u_{n}),\ t\in(0,1),\\ u_{i}(0)=\sum_{j=1}^m a_ju_i(x_j),\ u_{i}(1)=\sum_{j=1}^m b_ju_i(x_j), \end{array}\right. i=1,\ldots,n.\] The approaches used are based on variational methods and critical point theory.

Keywords: multiple solutions, multi-point boundary value problem, critical point theory.

Mathematics Subject Classification: 34B10, 34B15.

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  • John R. Graef
  • University of Tennessee at Chattanooga, Department of Mathematics, Chattanooga, TN 37403, USA
  • Shapour Heidarkhani
  • Razi University, Faculty of Sciences, Department of Mathematics, Kermanshah 67149, Iran
  • Institute for Research in Fundamental Sciences (IPM), School of Mathematics, P.O. Box 19395-5746, Tehran, Iran
  • Lingju Kong
  • Department of Mathematics, University of Tennessee at Chattanooga, Chattanooga, TN 37403, USA
  • Received: 2012-08-29.
  • Revised: 2012-10-23.
  • Accepted: 2012-10-25.
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Cite this article as:
John R. Graef, Shapour Heidarkhani, Lingju Kong, Multiple solutions for systems of multi-point boundary value problems, Opuscula Math. 33, no. 2 (2013), 293-306, http://dx.doi.org/10.7494/OpMath.2013.33.2.293

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