Multi-bump Solutions for a Strongly Degenerate Problem with Exponential Growth in RN

被引：0

作者：

dos Santos, Jefferson Abrantes ^{[1
]}

Figueiredo, Giovany M. ^{[2
]}

Severo, Uberlandio B. ^{[3
]}

机构：

[1] Univ Fed Campina Grande, Unidade Acad Matemat UAMat, BR-58429900 Campina Grande, PB, Brazil

[2] Univ Brasilia, Dept Matemat, BR-70910900 Brasilia, DF, Brazil

[3] Univ Fed Paraiba, Dept Matemat, BR-58051900 Joao Pessoa, PB, Brazil

来源：

JOURNAL OF GEOMETRIC ANALYSIS | 2024年 / 34卷 / 08期

关键词：

Orlicz-Sobolev spaces; Critical exponential growth; Multi-bump solutions; Variational methods; POSITIVE SOLUTIONS; MULTIPLICITY; EXISTENCE; EQUATIONS;

D O I：

10.1007/s12220-024-01687-6

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we study a class of strongly degenerate problems with critical exponential growth in R-N, N >= 2. We do not assume ellipticity condition on the operator and thus the maximum principle given by Lieberman (Commun Partial Differ Equ 16:311-361,1991) can not be accessed. Therefore, a careful and delicate analysis is necessary and some ideas can not be applied in our scenario. The arguments developed in this paper are variational and our main result completes the study made in the current literature about the subject. Moreover, when N=2 or N=3 the solutions model the slow steady-state flow of a fluid of Prandtl-Eyring type.

引用

页数：51

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[37] Multi-bump Solutions for a Strongly Degenerate Problem with Exponential Growth in RN\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {R}^N$$\end{document}
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