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Research Article | Open Access

Quasilinear elliptic equations with unbalanced growth and singular perturbation

Wulong Liu1, Huayuan Feng1, Yingjie Sun1, Patrick Winkert2( )
School of Mathematics and Information Sciences, Yantai University, Yantai 264005, China
Technische Universität Berlin, Institut für Mathematik, Straße des 17. Juni 136, 10623 Berlin, Germany
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Abstract

In this paper, we study parametric quasilinear elliptic equations driven by the double phase operator, where the right-hand side consists of a singular term and a sublinear term. By combining a new Hopf's Lemma with truncation techniques and an abstract critical point theorem, we establish the existence of three bounded positive solutions and provide an explicit upper bound for the parameter.

Keywords

double phase operatorHopf's Lemmamultiple solutionssingular problemsunbalanced growth

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Electronic Research Archive
Volume 33 Issue 11,
November 2025
Pages 6720-6741
DOI: 10.3934/era.2025297

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Cite this article:
Liu W, Feng H, Sun Y, et al. Quasilinear elliptic equations with unbalanced growth and singular perturbation. Electronic Research Archive, 2025, 33(11): 6720-6741. https://doi.org/10.3934/era.2025297

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Received: 20 September 2025
Revised: 31 October 2025
Accepted: 06 November 2025
Published: 13 November 2025
©2025 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)