AN UNBOUNDED CRITICAL POINT THEORY FOR A CLASS OF NON-DIFFERENTIABLE FUNCTIONALS AND ITS APPLICATION

Ziqing Yuan; Xiaoping Wang; Qinqin Zhang

doi:10.11948/20220143

2022 Volume 12 Issue 3

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Ziqing Yuan, Xiaoping Wang, Qinqin Zhang. AN UNBOUNDED CRITICAL POINT THEORY FOR A CLASS OF NON-DIFFERENTIABLE FUNCTIONALS AND ITS APPLICATION[J]. Journal of Applied Analysis & Computation, 2022, 12(3): 1104-1117. doi: 10.11948/20220143

Citation:

Ziqing Yuan, Xiaoping Wang, Qinqin Zhang. AN UNBOUNDED CRITICAL POINT THEORY FOR A CLASS OF NON-DIFFERENTIABLE FUNCTIONALS AND ITS APPLICATION[J]. Journal of Applied Analysis & Computation, 2022, 12(3): 1104-1117. doi: 10.11948/20220143

AN UNBOUNDED CRITICAL POINT THEORY FOR A CLASS OF NON-DIFFERENTIABLE FUNCTIONALS AND ITS APPLICATION

1.
Department of Mathematics, Shaoyang University, Shaoyang, Hunan, 422000, China
2.
Department of Mathematics and Statistics, Xiangnan University, Chenzhou, Hunan, 423000, China
3.
Department of Foundational Courses, Software Engineering Institute of Guangzhou, Guangzhou, 510900, China

Dedicated to Professor Jibin Li on the occasion of his 80th birthday.
Corresponding author: Email: wxp31415@163.com(X. Wang)
Fund Project: The authors were supported by the National Natural Science Foundation of China (Nos. 11901126, 12071395), the Scientific Research fund of Hunan provincial Education Department (No. 20B524) and the Guizhou technology plan project(No. [2020]1Y004)

Abstract

Abstract

In this paper, a nonsmooth version of multiple critical point theorem is established by adopting the framework of nonsmooth analysis theory. Then an application of this theorem to a discontinuous quasilinear Schrödinger equation is presented. Some continuous results are extended to discontinuous cases.
- Nonsmooth analysis /
- quasilinear Schrödinger equation /
- differential inclusion
MSC: 35J85, 47J30, 49J52

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References

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