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

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-06-08 DOI:10.1016/j.nonrwa.2024.104154

Edir Júnior Ferreira Leite , Marcos Montenegro

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 $q < p - 1$ and at the infinity as $u^{r}$ with $r > p - 1$ . 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

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

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