Multiple solutions to a quasilinear Schrödinger equation with Robin boundary condition

Yin Deng; Gao Jia; Fanglan Li; Yin Deng; Gao Jia; Fanglan Li

doi:10.3934/math.2020248

AIMS Mathematics

2020, Volume 5, Issue 4: 3825-3839. doi: 10.3934/math.2020248

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Research article

Multiple solutions to a quasilinear Schrödinger equation with Robin boundary condition

1.
Business School, University of Shanghai for Science and Technology, Shanghai, 200093, China
2.
College of Science, University of Shanghai for Science and Technology, Shanghai, 200093, China
3.
Shanghai University of Medicine and Health Sciences, Shanghai, 201318, China

Received: 30 December 2019 Accepted: 01 April 2020 Published: 21 April 2020
MSC : 35J60, 35J20

We study a quasilinear Schrödinger equation with Robin boundary condition. Using the variational methods and the truncation techniques, we prove the existence of two positive solutions when the parameter λ is large enough. We also establish the existence of infinitely many high energy solutions by using Fountain Theorem when λ > 1.
- quasilinear Schrödinger equation,
- Robin boundary,
- multiple solutions,
- Fountain Theorem
Citation: Yin Deng, Gao Jia, Fanglan Li. Multiple solutions to a quasilinear Schrödinger equation with Robin boundary condition[J]. AIMS Mathematics, 2020, 5(4): 3825-3839. doi: 10.3934/math.2020248

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Abstract

We study a quasilinear Schrödinger equation with Robin boundary condition. Using the variational methods and the truncation techniques, we prove the existence of two positive solutions when the parameter λ is large enough. We also establish the existence of infinitely many high energy solutions by using Fountain Theorem when λ > 1.

References

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