Critical point approaches to Gradient-Type systems on the Sierpiński Gasket

Fangfang Liao; Shapour Heidarkhani; Ghasem A. Afrouzi; Amjad Salari

doi:10.11948/2019.314

2019 Volume 9 Issue 1

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Fangfang Liao, Shapour Heidarkhani, Ghasem A. Afrouzi, Amjad Salari. Critical point approaches to Gradient-Type systems on the Sierpiński Gasket[J]. Journal of Applied Analysis & Computation, 2019, 9(1): 314-331. doi: 10.11948/2019.314

Citation:

Fangfang Liao, Shapour Heidarkhani, Ghasem A. Afrouzi, Amjad Salari. Critical point approaches to Gradient-Type systems on the Sierpiński Gasket[J]. Journal of Applied Analysis & Computation, 2019, 9(1): 314-331. doi: 10.11948/2019.314

Critical point approaches to Gradient-Type systems on the Sierpiński Gasket

1.
Department of Mathematics, Southeast University, Nanjing 210096, China
2.
Department of Mathematics, Shanghai Normal University, Shanghai 200234, China
3.
Department of Mathematics, Faculty of Sciences, Razi University, 67149 Kermanshah, Iran
4.
Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran

Corresponding author: Email address: sh.heidarkhani@yahoo.com (S. Heidarkhani)
Fund Project: Fang-Fang Liao was supported by the National Natural Science Foundation of China (Grant No. 11701375) and the Natural Science Foundation of Shanghai Normal University (Grant No. SK201709). Ghasem A. Afrouzi and Amjad Salari were supported by Iran National Science Foundation (Grant No. 96014557)

Abstract

Abstract

We investigate the existence of multiple solutions for parametric quasi-linear systems of the gradient-type on the Sierpiński gasket. We give some new criteria to guarantee that the systems have at least three weak solutions by using a variational method and some critical points theorems due to Ricceri. We extend and improve some recent results. Finally, we give two examples to illustrate the main results.
- Gradient-Type systems /
- Sierpiń /
- ski gasket /
- nonlinear elliptic equation /
- variational methods /
- critical point theory
MSC: 35J20, 28A80, 35J25, 35J60, 47J30, 49J52

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References

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