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Schrodinger Equation with Asymptotically Linear Nonlinearities
Journal article   Open access  Peer reviewed

Schrodinger Equation with Asymptotically Linear Nonlinearities

Amel El-Abed, Abir Amor Ben Ali and Makkia Dammak
Filomat, Vol.36(2), pp.629-639
01/01/2022

Abstract

Mathematics Mathematics, Applied Physical Sciences Science & Technology
In this paper, we investigate a quasilinear Schrodinger problem under Dirichlet boundary condi-tion 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.
url
https://doi.org/10.2298/FIL2202629EView
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