Multiplicity and concentration results for some nonlinear Schrödinger equations with the fractional p-Laplacian

Vincenzo Ambrosio; Teresa Isernia

doi:10.3934/dcds.2018254

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2018, Volume 38, Issue 11: 5835-5881. Doi: 10.3934/dcds.2018254

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Multiplicity and concentration results for some nonlinear Schrödinger equations with the fractional p-Laplacian

Vincenzo Ambrosio^1, and
Teresa Isernia^2,

1.
Department of Mathematics, EPFL SB CAMA, Station 8 CH-1015 Lausanne, Switzerland
2.
Dipartimento di Ingegneria Industriale e Scienze Matematiche, Università Politecnica delle Marche, Via Brecce Bianche, 12, 60131 Ancona, Italy

Received: January 31, 2018

Revised: June 30, 2018

Published: August 2018

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Abstract

We consider a class of parametric Schrödinger equations driven by the fractional $p$-Laplacian operator and involving continuous positive potentials and nonlinearities with subcritical or critical growth. Using variational methods and Ljusternik-Schnirelmann theory, we study the existence, multiplicity and concentration of positive solutions for small values of the parameter.

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Mathematics Subject Classification: Primary: 47G20, 35R11; Secondary: 35A15, 58E05.

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