Quasilinear elliptic equations with unbalanced growth and singular perturbation

Wulong Liu; Huayuan Feng; Yingjie Sun; Patrick Winkert; Wulong Liu; Huayuan Feng; Yingjie Sun; Patrick Winkert

doi:10.3934/era.2025297

Electronic Research Archive

2025, Volume 33, Issue 11: 6720-6741. doi: 10.3934/era.2025297

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Quasilinear elliptic equations with unbalanced growth and singular perturbation

1.
School of Mathematics and Information Sciences, Yantai University, Yantai 264005, China
2.
Technische Universität Berlin, Institut für Mathematik, Straße des 17. Juni 136, 10623 Berlin, Germany
Dedicated to Professor Patrizia Pucci on the occasion of her 70th birthday.

Received: 20 September 2025 Revised: 31 October 2025 Accepted: 06 November 2025 Published: 13 November 2025

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.
- double phase operator,
- Hopf's Lemma,
- multiple solutions,
- singular problems,
- unbalanced growth
Citation: Wulong Liu, Huayuan Feng, Yingjie Sun, Patrick Winkert. Quasilinear elliptic equations with unbalanced growth and singular perturbation[J]. Electronic Research Archive, 2025, 33(11): 6720-6741. doi: 10.3934/era.2025297

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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.

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