Nontrivial solutions to affine p-Laplace equations via a perturbation strategy

IF 1.8 3区数学 Q1 MATHEMATICS, APPLIED

Nonlinear Analysis-Real World Applications Pub Date : 2024-06-08 DOI:10.1016/j.nonrwa.2024.104154

Edir Júnior Ferreira Leite , Marcos Montenegro

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引用次数: 0

Abstract

This paper is concerned with the existence of nontrivial solutions for affine $p$ -Laplace equations involving subcritical nonlinearities behaving at $u = 0$ as $u^{q}$ with $q p - 1$ . Since local Palais–Smale compactness for affine energy type functionals is an open hard question, the problem is overcome by means of a perturbative approach using the space norm. Mountain-pass critical points are constructed from a limit process of corresponding ones in the modified affine context. Compactness and stability of MP solution sets are also addressed.

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通过扰动策略实现仿射 p 拉普拉斯方程的非微观解

本文关注的是仿射 p-Laplace 方程的非微观解的存在性问题，该方程涉及亚临界非线性，在 u=0 时表现为 uq（含 q<p-1），在无穷远处表现为 ur（含 r>p-1）。由于仿射能量型函数的局部 Palais-Smale compactness 是一个未解决的难题，因此通过使用空间规范的扰动方法来解决这个问题。根据修正仿射背景下相应临界点的极限过程，构建了穿山临界点。同时还解决了 MP 解集的紧凑性和稳定性问题。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Nonlinear Analysis-Real World Applications 数学-应用数学

CiteScore

3.80

自引率

5.00%

发文量

176

审稿时长

59 days

期刊介绍： Nonlinear Analysis: Real World Applications welcomes all research articles of the highest quality with special emphasis on applying techniques of nonlinear analysis to model and to treat nonlinear phenomena with which nature confronts us. Coverage of applications includes any branch of science and technology such as solid and fluid mechanics, material science, mathematical biology and chemistry, control theory, and inverse problems. The aim of Nonlinear Analysis: Real World Applications is to publish articles which are predominantly devoted to employing methods and techniques from analysis, including partial differential equations, functional analysis, dynamical systems and evolution equations, calculus of variations, and bifurcations theory.