| Full text | |
| Author(s): |
de Araujo, Anderson L. A.
;
Ercole, Grey
;
Montenegro, Marcelo
Total Authors: 3
|
| Document type: | Journal article |
| Source: | Results in Mathematics; v. 79, n. 1, p. 12-pg., 2024-02-01. |
| Abstract | |
We show the existence of a positive solution up\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$u_{p}$$\end{document} for a Dirichlet p-Laplacian problem with nonlinearity involving an exponential term that can be supercritical. We determine the asymptotic behavior of up\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$u_{p}$$\end{document} as p -> 1+\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$p\rightarrow 1<^>{+}$$\end{document} and p ->+infinity\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$p\rightarrow +\infty $$\end{document}, which are related to the Cheeger constant and the distance function to the boundary, respectively. Furthermore, we also prove a nonexistence result concerning the range of the parameter lambda\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\lambda $$\end{document}. (AU) | |