Some useful tools in the study of nonlinear elliptic problems

Papageorgiou, Nikolaos S.; Radulescu, Vicentiu

Some useful tools in the study of nonlinear elliptic problems

Files

1s2.0S0723086924000835main.pdf(496.73 KB)

Date

2024-12-05

Authors

Papageorgiou, Nikolaos S.

Radulescu, Vicentiu

ORCID

0000-0003-4615-5537

Publisher

Elsevier

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Abstract

This paper gives an overview of some basic aspects concerning the qualitative analysis of nonlinear, nonhomogeneous elliptic problems. We are concerned with two classes of elliptic equations with Dirichlet boundary condition. The first problem is driven by a general nonhomogeneous differential operator, which includes several usual operators (such as the (p,q)-Laplace operator introduced by P. Marcellini). Next, we focus on differential operators with unbalanced growth in the nonautonomous case. Our analysis will point out some relevant differences between balanced and unbalanced growth problems. The presentation is done in the context of Dirichlet problems but a similar analysis can be developed for other boundary conditions, such as Neumann or Robin.

Keywords

(p, q)-equation, Constant sign and nodal solutions, Dirichlet boundary condition, Double phase energy, Nonhomogeneous differential operator, Nonlinear elliptic equation

Citation

EXPOSITIONES MATHEMATICAE. 2024, vol. 42, issue 6, p. 1-27.
https://www.sciencedirect.com/science/article/pii/S0723086924000835

Document type

Peer-reviewed

Document version

Published version

Language of document

en

Document licence

Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International
http://creativecommons.org/licenses/by-nc-nd/4.0/