EXISTENCE OF SOLUTIONS TO A GENERALIZED KADOMTSEV-PETVIASHVILI EQUATION WITH A POTENTIAL AND CONCAVE-CONVEX NONLINEARITY

Jiaoping Chen; Jianqing Chen

doi:10.11948/20230469

2024 Volume 14 Issue 3

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Article navigation > Journal of Applied Analysis & Computation > 2024 > 14(3): 1820-1830

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Jiaoping Chen, Jianqing Chen. EXISTENCE OF SOLUTIONS TO A GENERALIZED KADOMTSEV-PETVIASHVILI EQUATION WITH A POTENTIAL AND CONCAVE-CONVEX NONLINEARITY[J]. Journal of Applied Analysis & Computation, 2024, 14(3): 1820-1830. doi: 10.11948/20230469

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Jiaoping Chen, Jianqing Chen. EXISTENCE OF SOLUTIONS TO A GENERALIZED KADOMTSEV-PETVIASHVILI EQUATION WITH A POTENTIAL AND CONCAVE-CONVEX NONLINEARITY[J]. Journal of Applied Analysis & Computation, 2024, 14(3): 1820-1830. doi: 10.11948/20230469

EXISTENCE OF SOLUTIONS TO A GENERALIZED KADOMTSEV-PETVIASHVILI EQUATION WITH A POTENTIAL AND CONCAVE-CONVEX NONLINEARITY

Jiaoping Chen^1,,
Jianqing Chen^1, ,

1.
School of Mathematics and Statistics, Fujian Normal University, Fuzhou 350117, China

Author Bio: Email: 1131643863@qq.com(Jiaoping Chen)
Corresponding author: Email: chenjq_iapcm@126.com(Jianqing Chen)

Abstract

Abstract

In this paper, we firstly prove the existence of infinitely many solutions with positive energy to a class of generalized Kadomtsev-Petviashvili equation with a potential and concave-convex nonlinearity. Secondly, with the help of genus, we are able to prove the existence of infinitely many solutions with negative energy for a suitable parameter $ \lambda $. Our results can be looked on as a generalization to previous works in the literature.
- Anisotropic Sobolev embedding /
- generalized Kadomtsev-Petviashvili equation /
- concave-convex nonlinearity /
- variational method
MSC: 35B40, 35J20

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References

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