Quasilinear Dirichlet problems with competing operators and convection-Reference-Cited by-同舟云学术

Quasilinear Dirichlet problems with competing operators and convection

Published:2020-01-01 Issue:1 Volume:18 Page:1510-1517
ISSN:2391-5455
Container-title:Open Mathematics
language:en
Short-container-title:

Author:

Motreanu Dumitru¹²

Affiliation:

1. Department of Mathematics, University of Perpignan , 66860 Perpignan , France

2. College of Science, Yulin Normal University , Yulin , People’s Republic of China

Abstract

Abstract The paper deals with a quasilinear Dirichlet problem involving a competing (p,q)-Laplacian and a convection term. Due to the lack of ellipticity, monotonicity and variational structure, the known methods to find a weak solution are not applicable. We develop an approximation procedure permitting to establish the existence of solutions in a generalized sense. If in place of competing (p,q)-Laplacian we consider the usual (p,q)-Laplacian, our results ensure the existence of weak solutions.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/math-2020-0112/pdf

Reference5 articles.

1. Zhenhai Liu, Roberto Livrea, Dumitru Motreanu, and Shengda Zeng, Variational differential inclusions without ellipticity condition, Electron. J. Qual. Theory Differ. Equ. 43 (2020), 1–17, 10.14232/ejqtde.2020.1.43.

2. Andrea Cianchi and Vladimir Maz’ya, Global gradient estimates in elliptic problems under minimal data and domain regularity, Commun. Pure Appl. Anal. 14 (2015), no. 1, 285–311, 10.3934/cpaa.2015.14.285.

3. Dumitru Motreanu, Nonlinear Differential Problems with Smooth and Nonsmooth Constraints, Academic Press, London, 2018.

4. Siegfried Carl, Vy Koy Le, and Dumitru Motreanu, Nonsmooth Variational Problems and Their Inequalities: Comparison Principles and Applications, Springer Monographs in Mathematics, Springer, New York, 2007.

5. Ralph E. Showalter, Monotone Operators in Banach Space and Nonlinear Partial Differential Equations, Mathematical Surveys and Monographs, vol. 49, American Mathematical Society, Providence, RI, 1997.

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