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

Xiaojie Guo; Zhiqing Han; Xiaojie Guo; Zhiqing Han

doi:10.3934/math.20231417

AIMS Mathematics

2023, Volume 8, Issue 11: 27684-27711. doi: 10.3934/math.20231417

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Research article

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

Received: 10 July 2023 Revised: 20 September 2023 Accepted: 25 September 2023 Published: 07 October 2023
MSC : 35J20, 35J62, 35Q35

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.
- quasilinear Schrödinger equation,
- concave-convex nonlinearities,
- vanishing potentials,
- positive solutions,
- mountain pass theorem
Citation: Xiaojie Guo, Zhiqing Han. Existence of solutions to a generalized quasilinear Schrödinger equation with concave-convex nonlinearities and potentials vanishing at infinity[J]. AIMS Mathematics, 2023, 8(11): 27684-27711. doi: 10.3934/math.20231417

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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.

References

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