$N$-Laplacian equations in $\mathbb{R}^N$ with critical growth

B. do Ó, João Marcos

Abstr. Appl. Anal., Tome 2 (1997) no. 1-2, p. 301-315 / Harvested from Project Euclid

Résumé

We study the existence of nontrivial solutions to the following problem: $\begin{cases}u\in W^{1,N}(\mathbb{R}^N),u\geq 0\mathrm{and}-div(|\nabla u|^{N-2}\nabla u)+ a(x)|u|^{N-2}u = f(x,u)\mathrm{in}\mathbb{R}^N(N \geq 2),\end{cases}$$ where $a$ is a continuous function which is coercive, i.e., $a(x)\rightarrow\infty\mathrm{as}|x|\rightarrow\infty$ and the nonlinearity $f$ behaves like $\exp(\alpha|u|^{N/(N-1)})$ when $|u|\rightarrow\infty$ .

Publié le : 1997-05-14
Classification: Elliptic equations, $p$-Laplacian, critical growth, Mountain Pass theorem, Trudinger-Moser inequality, 35A15, 35J60

@article{1050355240,
     author = {B. do \'O, Jo\~ao Marcos},
     title = {$N$-Laplacian equations in $\mathbb{R}^N$ with critical growth},
     journal = {Abstr. Appl. Anal.},
     volume = {2},
     number = {1-2},
     year = {1997},
     pages = { 301-315},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1050355240}
}

B. do Ó, João Marcos. $N$-Laplacian equations in $\mathbb{R}^N$ with critical growth. Abstr. Appl. Anal., Tome 2 (1997) no. 1-2, pp.  301-315. http://gdmltest.u-ga.fr/item/1050355240/