Existence and multiplicity of solutions to N-Laplacian equation with discontinuous exponential growth in ℝN

Mengyuan Xi

doi:10.59400/adecp3103

Existence and multiplicity of solutions to N-Laplacian equation with discontinuous exponential growth in ℝN

Mengyuan Xi School of Mathematical Sciences, Chongqing Normal University, Chongqing 401331, China

Article ID: 3103

Keywords: trudinger-moser inequality; variational methods; non-smooth analysis; mountain pass theorem; free boundary problems; discontinuous nonlinearities

Abstract

This research explores the existence and multiplicity of solutions to N-Laplacian equations with discontinuous exponential nonlinearities in the whole Euclidean space. Through combining symmetric rearrangement techniques and variational methods for non-differentiable functionals, it identifies sufficient conditions for the existence of weak solutions when perturbation parameters are small, and uncovers the rich solution structure caused by discontinuous growth and non-smooth operators.These studies connect critical Sobolev growth and exponential nonlinearities, which is an important link in phase transition models and nonlinear analysis.We have proven the existence and multiplicity of weak solutions for the N-Laplacian equation with discontinuous exponential growth . Notably, when the perturbation parameter is sufficiently small, there exist at least multiple weak solutions, which stem from the interaction between the discontinuous exponential nonlinearity and the N-Laplacian operator. Compared to previous findings, our results extend the existing literature on elliptic equations with critical growth and discontinuous nonlinearities. Additionally, the combination of priori estimates with non-differentiable variational methods constitutes a novel approach, distinct from traditional techniques in earlier studies.

Published

2025-09-30

How to Cite

Xi, M. (2025). Existence and multiplicity of solutions to N-Laplacian equation with discontinuous exponential growth in ℝN . Advances in Differential Equations and Control Processes, 32(3). https://doi.org/10.59400/adecp3103

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Vol. 32 No. 3 (2025)

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Article

This work is licensed under a Creative Commons Attribution 4.0 International License.

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