Multiplicity of solutions for critical quasilinear Schrödinger equations using a linking structure

Edcarlos D. Silva; Jefferson S. Silva

doi:10.3934/dcds.2020234

Article Contents

2020, Volume 40, Issue 9: 5441-5470. Doi: 10.3934/dcds.2020234

This issue Previous Article Time periodic solution to a coupled chemotaxis-fluid model with porous medium diffusion Next Article Global existence and convergence of nondimensionalized incompressible Navier-Stokes equations in low Froude number regime

Multiplicity of solutions for critical quasilinear Schrödinger equations using a linking structure

Edcarlos D. Silva^, and
Jefferson S. Silva

Universidade Federal de Goiás, 74001-970, Goiás-GO, Brazil

^* Corresponding author: Edcarlos D. Silva
^* Corresponding author: Edcarlos D. Silva

Received: October 31, 2019

Revised: March 31, 2020

Published: June 2020

The first author is partially supported by CNPq grant 429955/2018-9

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Abstract

It is established multiplicity of solutions for critical quasilinear Schrödinger equations defined in the whole space using a linking structure. The main difficulty comes from the lack of compactness of Sobolev embedding into Lebesgue spaces. Moreover, the potential is bounded from below and above by positive constants. In order to overcome these difficulties we employ Lions Concentration Compactness Principle together with some fine estimates for the energy functional restoring some kind of compactness.

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Mathematics Subject Classification: Primary: 35J10, 35J20, 35J62; Secondary: 35J15, 35J25.

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