| Full text | |
| Author(s): |
De Paiva, Francisco Odair
;
Kryszewski, Wojciech
;
Szulkin, Andrzej
Total Authors: 3
|
| Document type: | Journal article |
| Source: | Proceedings of the American Mathematical Society; v. 145, n. 11, p. 4783-4794, NOV 2017. |
| Web of Science Citations: | 4 |
| Abstract | |
We study the Schrodinger equations -Delta u + V (x) u = f( x, u) in R-N and -Delta u -lambda u = f( x, u) in a bounded domain Omega subset of R-N. We assume that f is superlinear but of subcritical growth and u bar right arrow f( x, u)/vertical bar u vertical bar is nondecreasing. In R-N we also assume that V and f are periodic in x1,..., xN. We show that these equations have a ground state and that there exist infinitely many solutions if f is odd in u. Our results generalize those by Szulkin and Weth {[}J. Funct. Anal. 257 (2009), 3802- 3822], where u bar right arrow f( x, u)/vertical bar u vertical bar was assumed to be strictly increasing. This seemingly small change forces us to go beyond methods of smooth analysis. (AU) | |
| FAPESP's process: | 15/10545-0 - Elliptic Problems with Indefinite Weights |
| Grantee: | Francisco Odair Vieira de Paiva |
| Support Opportunities: | Scholarships abroad - Research |