AIMS Mathematics, 2020, 5(4): 3825-3839. doi: 10.3934/math.2020248.

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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

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.
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Keywords 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. AIMS Mathematics, 2020, 5(4): 3825-3839. doi: 10.3934/math.2020248

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