2022 Fourth-order elliptic problems involving concave-superlinear nonlinearities
Edcarlos D. Silva, Thiago R. Cavalcante
Topol. Methods Nonlinear Anal. 60(2): 581-600 (2022). DOI: 10.12775/TMNA.2022.011

Abstract

The existence of solutions for a huge class of superlinear elliptic problems involving fourth-order elliptic problems defined on bounded domains under Navier boundary conditions is established. To this end we do not apply the well-known Ambrosetti-Rabinowitz condition. Instead, we assume that the nonlinear term is nonquadratic at infinity. Furthermore, the nonlinear term is a concave-superlinear function which can be indefinite in sign. In order to apply variational methods we employ some delicate arguments recovering some kind of compactness.

Citation

Download Citation

Edcarlos D. Silva. Thiago R. Cavalcante. "Fourth-order elliptic problems involving concave-superlinear nonlinearities." Topol. Methods Nonlinear Anal. 60 (2) 581 - 600, 2022. https://doi.org/10.12775/TMNA.2022.011

Information

Published: 2022
First available in Project Euclid: 11 December 2022

MathSciNet: MR4563249
zbMATH: 1512.35225
Digital Object Identifier: 10.12775/TMNA.2022.011

Keywords: concave-superlinear elliptic problems , Fourth-order elliptic problems , nonquadraticity condition , variational methods

Rights: Copyright © 2022 Juliusz P. Schauder Centre for Nonlinear Studies

JOURNAL ARTICLE
20 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

Vol.60 • No. 2 • 2022
Back to Top