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Research Article | Open Access

Existence of solutions to a generalized quasilinear Schrödinger equation with concave-convex nonlinearities and potentials vanishing at infinity

Xiaojie Guo, Zhiqing Han( )
School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China
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Abstract

In this paper, we investigate the existence of solutions to a generalized quasilinear Schrödinger equation with concave-convex nonlinearities and potentials vanishing at infinity. Using the mountain pass theorem, we get the existence of a positive solution.

Keywords

quasilinear Schrödinger equationconcave-convex nonlinearitiesvanishing potentialspositive solutionsmountain pass theorem
CLC number: 35J20, 35J62, 35Q35

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AIMS Mathematics
Volume 8 Issue 11,
November 2023
Pages 27684-27711
DOI: 10.3934/math.20231417

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Cite this article:
Guo X, Han Z. Existence of solutions to a generalized quasilinear Schrödinger equation with concave-convex nonlinearities and potentials vanishing at infinity. AIMS Mathematics, 2023, 8(11): 27684-27711. https://doi.org/10.3934/math.20231417

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Received: 10 July 2023
Revised: 20 September 2023
Accepted: 25 September 2023
Published: 15 November 2023
©2023 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)