Positive solutions for resonant singular non-autonomous $ (p, q) $-equations

Nikolaos S. Papageorgiou; Dongdong Qin; Vicenţiu D. Rădulescu

doi:10.3934/dcdsb.2024165

Article Contents

2025, Volume 30, Issue 11: 4426-4441. Doi: 10.3934/dcdsb.2024165

This issue Previous Article Existence of solutions to nonlinear

$ 2n $

-th order discrete boundary value problem via variational method Next Article Bistability and chaos in the discrete two-gene Andrecut-Kauffman model

Positive solutions for resonant singular non-autonomous $ (p, q) $-equations

1.
National Technical University, Department of Mathematics, Zografou Campus, Athens 15780, Greece
2.
School of Mathematics and Statistics, HNP-LAMA, Central South University, Changsha 410083, Hunan, China
3.
Department of Mathematics, University of Craiova, 200585 Craiova, Romania
4.
Faculty of Applied Mathematics, AGH University of Kraków, al. Mickiewicza 30, 30-059 Kraków, Poland
5.
Simion Stoilow Institute of Mathematics of the Romanian Academy, 010702 Bucharest, Romania
6.
Brno University of Technology, Faculty of Electrical Engineering and Communication, Technická 3058/10, Brno 61600, Czech Republic
7.
Department of Mathematics, Zhejiang Normal University, Jinhua 321004, Zhejiang, China

^* Corresponding author: Dongdong Qin
^* Corresponding author: Dongdong Qin

Received: September 2024

Revised: November 2024

Early access: November 2024

Published: November 2025

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Abstract

We consider a singular elliptic equation, driven by the non-autonomous ($ p, q $)-operator and with a resonant perturbation. Using variational tools together with truncation and comparison techniques, we show that if the $ L^{\infty} $-norm of the coefficient of the singular term is small enough, then the problem has at least two positive smooth solutions.

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Mathematics Subject Classification: 35J20, 35J75, 35J92.

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References

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