Periodic solutions for a differential inclusion problem involving the p(t)-Laplacian-Reference-Cited by-同舟云学术

Periodic solutions for a differential inclusion problem involving the p(t)-Laplacian

Published:2020-12-19 Issue:1 Volume:10 Page:799-815
ISSN:2191-950X
Container-title:Advances in Nonlinear Analysis
language:en
Short-container-title:

Author:

Chen Peng¹²,Tang Xianhua³

Affiliation:

1. College of Science, China Three Gorges University , Yichang , , P.R. China

2. Three Gorges Mathematical Research Center, China Three Gorges University , Yichang , , P.R. China

3. School of Mathematics and Statistics, Central South University , Changsha , , P.R. China

Abstract

Abstract In the present paper, we consider the nonlinear periodic systems involving variable exponent driven by p(t)-Laplacian with a locally Lipschitz nonlinearity. Our arguments combine the variational principle for locally Lipschitz functions with the properties of the generalized Lebesgue-Sobolev space. Applying the non-smooth critical point theory, we establish some new existence results.

Publisher

Walter de Gruyter GmbH

Subject

Analysis

Link

https://www.degruyter.com/document/doi/10.1515/anona-2020-0156/pdf

Reference42 articles.

1. S. N. Antontsev, S. I. Shmarev, A model porous medium equation with variable exponent of nonlinearity: Existence, uniqueness and localization properties of solutions, Nonlinear Anal. 60(2005), 515-545.

2. S. N. Antontsev, J. F. Rodrigues, On stationary thermo-rheological viscous flows, Ann. Univ. Ferrara Sez. VII Sci. Mat. 52(2006), 19-36.

3. K. C. Chang, Variational methods for nondifferentiable functions and their applications to partial differential equations, J. Math. Anal. Appl. 80(1981), no. 1, 102-129.

4. Y. Chen, S. Levine, M. Rao, Variable exponent, linear growth functionals in image restoration, SIAM J. Appl. Math. 66(2006), no. 4, 1383-1406.

5. F. H. Clarke, Optimization and Nonsmooth Analysis. Wiley, New York, 1993.

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