Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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EXISTENCE AND MULTIPLICITY OF WEAK SOLUTIONS FOR SOME p(x)-LAPLACIAN-LIKE PROBLEMS VIA VARIATIONAL METHODS

  • AFROUZI, G.A. (Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran) ;
  • SHOKOOH, S. (Department of Mathematics, Faculty of Sciences, Gonbad Kavous University) ;
  • CHUNG, N.T. (Department of Mathematics, Quang Binh University)
  • Received : 2016.01.17
  • Accepted : 2016.05.18
  • Published : 2017.01.30
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Abstract

Using variational methods, we study the existence and multiplicity of weak solutions for some p(x)-Laplacian-like problems. First, without assuming any asymptotic condition neither at zero nor at infinity, we prove the existence of a non-zero solution for our problem. Next, we obtain the existence of two solutions, assuming only the classical Ambrosetti-Rabinowitz condition. Finally, we present a three solutions existence result under appropriate condition on the potential F.

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References

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