Opuscula Math. 37, no. 3 (2017), 353-379

Opuscula Mathematica

Existence of three solutions for impulsive multi-point boundary value problems

Martin Bohner
Shapour Heidarkhani
Amjad Salari
Giuseppe Caristi

Abstract. This paper is devoted to the study of the existence of at least three classical solutions for a second-order multi-point boundary value problem with impulsive effects. We use variational methods for smooth functionals defined on reflexive Banach spaces in order to achieve our results. Also by presenting an example, we ensure the applicability of our results.

Keywords: multi-point boundary value problem, impulsive condition, classical solution, variational method, three critical points theorem.

Mathematics Subject Classification: 34B10, 34B15, 34A37.

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  • Martin Bohner
  • Department of Mathematics and Statistics, Missouri S&T, Rolla, MO 65409-0020, USA
  • Shapour Heidarkhani
  • Razi University, Faculty of Sciences, Department of Mathematics, 67149 Kermanshah, Iran
  • Amjad Salari
  • Razi University, Faculty of Sciences, Department of Mathematics, 67149 Kermanshah, Iran
  • Giuseppe Caristi
  • University of Messina, Department of Economics, Messina, Italy
  • Communicated by Marek Galewski.
  • Received: 2016-08-23.
  • Revised: 2016-12-07.
  • Accepted: 2016-12-08.
  • Published online: 2017-01-30.
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Cite this article as:
Martin Bohner, Shapour Heidarkhani, Amjad Salari, Giuseppe Caristi, Existence of three solutions for impulsive multi-point boundary value problems, Opuscula Math. 37, no. 3 (2017), 353-379, http://dx.doi.org/10.7494/OpMath.2017.37.3.353

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