HOMOCLINIC SOLUTIONS FOR FOURTH ORDER DIFFERENTIAL EQUATIONS WITH SUPERLINEAR NONLINEARITIES

Ziheng Zhang; Zhisu Liu

doi:10.11948/2018.66

2018 Volume 8 Issue 1

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Ziheng Zhang, Zhisu Liu. HOMOCLINIC SOLUTIONS FOR FOURTH ORDER DIFFERENTIAL EQUATIONS WITH SUPERLINEAR NONLINEARITIES[J]. Journal of Applied Analysis & Computation, 2018, 8(1): 66-80. doi: 10.11948/2018.66

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Ziheng Zhang, Zhisu Liu. HOMOCLINIC SOLUTIONS FOR FOURTH ORDER DIFFERENTIAL EQUATIONS WITH SUPERLINEAR NONLINEARITIES[J]. Journal of Applied Analysis & Computation, 2018, 8(1): 66-80. doi: 10.11948/2018.66

HOMOCLINIC SOLUTIONS FOR FOURTH ORDER DIFFERENTIAL EQUATIONS WITH SUPERLINEAR NONLINEARITIES

Ziheng Zhang¹,
Zhisu Liu²

1 Department of Mathematics, Tianjin Polytechnic University, Tianjin 300387, China;
2 School of Mathematics and Physics, University of South China, Hengyang, Hunan 421001, China

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Abstract

Abstract

In this paper we investigate the existence of homoclinic solutions for a class of fourth order differential equations with superlinear nonlinearities. Under some superlinear conditions weaker than the well-known (AR) condition, by using the variant fountain theorem, we establish one new criterion to guarantee the existence of infinitely many homoclinic solutions.
- Homoclinic solutions /
- critical point /
- variational methods /
- fountain theorem
MSC: 34C37;35A15;35B38

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References

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