Existence, multiplicity and numerical examples for Schrödinger systems with nonstandard p(x)-growth conditions

Abstract

In this paper, we deal with the Schrödinger’s problems, in the first part we study the theoretical side, we show the existence of at least three weak solutions, our main tools are based on variational inequalities, more precisely, using the three critical points theorem due to Ricceri, existence and multiplicity results are established. In the second part, we are interested in the application side, more exactly, we examine some computational problems on the discretization of finite elements of the p(x)-Laplacian, we propose a quasi-Newton minimization approach for the solution, our numerical tests show that these algorithms are able to resolve the problems with p(x)-Laplacian, for different values of p(x).

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Correspondence to Thiziri Chergui or Saadia Tas.

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Chergui, T., Tas, S. Existence, multiplicity and numerical examples for Schrödinger systems with nonstandard p(x)-growth conditions. Indian J Pure Appl Math 51, 413–437 (2020). https://doi.org/10.1007/s13226-020-0408-6

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Key words

  • Nonlinear boundary value problems
  • variable exponent sobolev space
  • multiplicity results
  • quasi-Newton minimization

2010 Mathematics Subject Classification

  • 34B15
  • 35A15
  • 65N38