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

Thiziri Chergui () and Saadia Tas ()
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Thiziri Chergui: University of Bejaia
Saadia Tas: University of Bejaia

Indian Journal of Pure and Applied Mathematics, 2020, vol. 51, issue 2, 413-437

Abstract: 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).

Keywords: Nonlinear boundary value problems; variable exponent sobolev space; multiplicity results; quasi-Newton minimization; 34B15; 35A15; 65N38 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s13226-020-0408-6

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