Positive ground state solutions for asymptotically periodic generalized quasilinear Schrödinger equations

Shulin Zhang; Shulin Zhang

doi:10.3934/math.2022061

AIMS Mathematics

2022, Volume 7, Issue 1: 1015-1034. doi: 10.3934/math.2022061

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Research article

Positive ground state solutions for asymptotically periodic generalized quasilinear Schrödinger equations

Shulin Zhang ^{1,2
,
,}

1.
Department of Mathematics, China University of Mining and Technology, Xuzhou 221116, China
2.
Department of Mathematics, Xuzhou Vocational Technology Academy of Finance and Economics, Xuzhou 221008, China

Received: 14 August 2021 Accepted: 08 October 2021 Published: 19 October 2021
MSC : 35J60, 35J50

In this paper, we study the existence of a positive ground state solution for a class of generalized quasilinear Schrödinger equations with asymptotically periodic potential. By the variational method, a positive ground state solution is obtained. Compared with the existing results, our results improve and generalize some existing related results.
- generalized quasilinear Schrödinger equations,
- asymptotically periodic,
- positive ground state solution,
- Nehari manifold method
Citation: Shulin Zhang. Positive ground state solutions for asymptotically periodic generalized quasilinear Schrödinger equations[J]. AIMS Mathematics, 2022, 7(1): 1015-1034. doi: 10.3934/math.2022061

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Abstract

In this paper, we study the existence of a positive ground state solution for a class of generalized quasilinear Schrödinger equations with asymptotically periodic potential. By the variational method, a positive ground state solution is obtained. Compared with the existing results, our results improve and generalize some existing related results.

References

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