Open AccessSchrödinger equation with asymptotically linear nonlinearities
Author(s) -
Amel El-Abeda,
Abir Amor Ben Ali,
Makkia Dammak
Publication year - 2022
Publication title -
filomat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 34
eISSN - 2406-0933
pISSN - 0354-5180
DOI - 10.2298/fil2202629e
Subject(s) - mathematics , dirichlet boundary condition , domain (mathematical analysis) , infinity , sequence (biology) , boundary value problem , boundary (topology) , nonlinear system , mathematical analysis , work (physics) , physics , quantum mechanics , genetics , biology
LRES, Faculty of Sciences of Tunis, University of Tunis El Manar, TunisiaEM makkia.dammak@gmail.com KW Asymptotically linear % variational method % Schr?dinger equations % Cerami sequenceKR nemaIn 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.