Nonexistence results for quasilinear elliptic problems with singular lower order terms

Asadollah Aghajani; Juha Kinnunen

doi:10.3934/dcds.2025069

Article Contents

2025, Volume 45, Issue 12: 4606-4629. Doi: 10.3934/dcds.2025069

This issue Previous Article Next Article Existence and characterization of ground states for fourth order nonlinear Schrödinger systems

Nonexistence results for quasilinear elliptic problems with singular lower order terms

Asadollah Aghajani^1, , and
Juha Kinnunen^2,

1.
School of Mathematics & Computer Science, Iran University of Science and Technology, Narmak, Tehran, Iran
2.
Department of Mathematics, Aalto University, P.O. Box 11100, FI-00076 Aalto, Finland

^*Corresponding author: Asadollah Aghajani
^*Corresponding author: Asadollah Aghajani

Received: November 2024

Revised: May 2025

Early access: May 2025

Published: December 2025

The work of the first author is based upon research funded by Iran National Science Foundation (INSF) under project No.4030766.

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Abstract

We establish a general Hardy-type inequality and apply it to investigate the nonexistence of positive solutions to the nonlinear elliptic problem

$ -\Delta u\ge \lambda \rho(x) u^p +\mu(x)\frac{|\nabla u|^s}{u^{\theta}}\quad \text{in}\ \Omega , $

in bounded domains in $ \mathbb{R}^N $, $ N \geq 2 $, and unbounded exterior domains in $ \mathbb{R}^N $, $ N \geq 3 $. We also discuss the corresponding results for the related systems of partial differential equations.

Keywords:

Mathematics Subject Classification: 35J62, 35A23, 35B09, 35B53, 47J10.

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