Existence results for Schrödinger type double phase variable exponent problems with convection term in $ \mathbb R^{N} $

Shuai Li; Tianqing An; Weichun Bu; Shuai Li; Tianqing An; Weichun Bu

doi:10.3934/math.2024417

AIMS Mathematics

2024, Volume 9, Issue 4: 8610-8629. doi: 10.3934/math.2024417

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Research article

Existence results for Schrödinger type double phase variable exponent problems with convection term in $ \mathbb R^{N} $

1.
School of Mathematics, Hohai University, Nanjing 210098, China
2.
School of Mathematics and Statistics, Fuyang Normal University, Fuyang 236037, China

Received: 06 January 2024 Revised: 05 February 2024 Accepted: 07 February 2024 Published: 29 February 2024
MSC : 35D30, 35J10, 35J91, 46E35

This paper was concerned with a new class of Schrödinger equations involving double phase operators with variable exponent in $ \mathbb R^{N} $. We gave the corresponding Musielak-Orlicz Sobolev spaces and proved certain properties of the double phase operator. Moreover, our main tools were the topological degree theory and Galerkin method, since the equation contained a convection term. By using these methods, we derived the existence of weak solution for the above problems. Our result extended some recent work in the literature.
- variable exponent,
- double phase problem,
- convection term,
- Galerkin method,
- topological degree
Citation: Shuai Li, Tianqing An, Weichun Bu. Existence results for Schrödinger type double phase variable exponent problems with convection term in $ \mathbb R^{N} $[J]. AIMS Mathematics, 2024, 9(4): 8610-8629. doi: 10.3934/math.2024417

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Abstract

This paper was concerned with a new class of Schrödinger equations involving double phase operators with variable exponent in $ \mathbb R^{N} $. We gave the corresponding Musielak-Orlicz Sobolev spaces and proved certain properties of the double phase operator. Moreover, our main tools were the topological degree theory and Galerkin method, since the equation contained a convection term. By using these methods, we derived the existence of weak solution for the above problems. Our result extended some recent work in the literature.

References

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