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Two classes of infinitely many solutions for fractional Schrödinger-Maxwell system with concave-convex power nonlinearities

Khiddi Mustapha

Journal of Mathematics and Applications

2022

Vol. 45

87--105

Employing critical theory and concentration estimates, we establish the existence of two classes of infinitely many weak solutions fractional Schrödinger-Poisson system involving critical Sobolev growth. The first classe of solutions with negative energy is found by using of notion genus while the second one contains infinitely many weak solutions with positive energy via Fountain theorem.

Infinitely many solutions for quasilinear Schrödinger equations with sign-changing nonlinearity without the aid of 4-superlinear at infinity

Khiddi Mustapha, Essafi Lakbir

Demonstratio Mathematica

2022

Vol. 55, nr 1

831--842

In this article, we will prove the existence of infinitely many solutions for a class of quasilinear Schrödinger equations without assuming the 4-superlinear at infinity on the nonlinearity. We achieve our goal by using the Fountain theorem.