Critical points approaches to a nonlocal elliptic problem driven by 𝑝(𝑥)-biharmonic operator-Reference-Cited by-同舟云学术

Critical points approaches to a nonlocal elliptic problem driven by 𝑝(𝑥)-biharmonic operator

Published:2021-11-06 Issue:1 Volume:29 Page:55-69
ISSN:1072-947X
Container-title:Georgian Mathematical Journal
language:en
Short-container-title:

Author:

Heidarkhani Shapour¹,Moradi Shahin²,Avci Mustafa³^ORCID

Affiliation:

1. Department of Mathematics , Faculty of Sciences , Razi University , 67149 Kermanshah , Iran

2. Department of Mathematics , Faculty of Mathematical Sciences , University of Mazandaran , Babolsar , Iran

3. Finance and Management Science , University of Saskatchewan , Saskatoon , SK, S7N 5A7 , Canada

Abstract

Abstract Differential equations with variable exponent arise from the nonlinear elasticity theory and the theory of electrorheological fluids. We study the existence of at least three weak solutions for the nonlocal elliptic problems driven by p ⁢ ( x )

p(x)

-biharmonic operator. Our technical approach is based on variational methods. Some applications illustrate the obtained results. We also provide an example in order to illustrate our main abstract results. We extend and improve some recent results.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/gmj-2021-2115/pdf

Reference33 articles.

1. S. N. Antontsev and S. I. Shmarev, A model porous medium equation with variable exponent of nonlinearity: Existence, uniqueness and localization properties of solutions, Nonlinear Anal. 60 (2005), no. 3, 515–545.

2. G. Bonanno and P. Candito, Non-differentiable functionals and applications to elliptic problems with discontinuous nonlinearities, J. Differential Equations 244 (2008), no. 12, 3031–3059.

3. G. Bonanno and G. D’Aguì, Multiplicity results for a perturbed elliptic Neumann problem, Abstr. Appl. Anal. 2010 (2010), Article ID 564363.

4. G. Bonanno and S. A. Marano, On the structure of the critical set of non-differentiable functions with a weak compactness condition, Appl. Anal. 89 (2010), no. 1, 1–10.

5. G. D’Aguì, S. Heidarkhani and G. Molica Bisci, Multiple solutions for a perturbed mixed boundary value problem involving the one-dimensional 𝑝-Laplacian, Electron. J. Qual. Theory Differ. Equ. 2013 (2013), Paper No. 24.

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