Schrödinger equation with asymptotically linear nonlinearities-Reference-Cited by-同舟云学术

Schrödinger equation with asymptotically linear nonlinearities

Published:2022 Issue:2 Volume:36 Page:629-639
ISSN:0354-5180
Container-title:Filomat
language:en
Short-container-title:Filomat

Author:

El-Abeda Amel¹,Ali Abir²,Dammak Makkia³

Affiliation:

1. Department of Mathematics, College of Science, Taibah University, Medina Saudi Arabia + Department of Mathematics, Faculty of Science, Tanta University, Tanta, Egypt

2. Department of Mathematics, Faculty of Sciences of Tunis, University of Tunis El Manar, Tunisia

3. Department of Mathematics, College of Science, Taibah University, Medina Saudi Arabia + Department of Mathematics, Faculty of Sciences, University of Sfax, Tunisia + Nonlinear Analysis and Geometric L

Abstract

LRES, Faculty of Sciences of Tunis, University of Tunis El Manar, Tunisia EM makkia.dammak@gmail.com KW Asymptotically linear % variational method % Schr?dinger equations % Cerami sequence KR nema In this paper, we investigate a quasilinear Schr?dinger problem under Dirichlet boundary condition in a regular domain with asymptotically linear nonlinearities. We use Cerami version of the mountain pass theorem to prove the existence of solution without using the Ambrosetti-Rabionovitz condition or any of its refinements. Then, we prove that the same techniques work when the nonlinearity is superlinear and subcritical at infinity.

Publisher

National Library of Serbia

Subject

General Mathematics

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