Back to Search
Start Over
On variational nonlinear equations with monotone operators
- Source :
- Advances in Nonlinear Analysis, Vol 10, Iss 1, Pp 289-300 (2020)
- Publication Year :
- 2020
- Publisher :
- De Gruyter, 2020.
-
Abstract
- Using monotonicity methods and some variational argument we consider nonlinear problems which involve monotone potential mappings satisfying condition (S) and their strongly continuous perturbations. We investigate when functional whose minimum is obtained by a direct method of the calculus of variations satisfies the Palais-Smale condition, relate minimizing sequence and Galerkin approximaitons when both exist, then provide structure conditions on the derivative of the action functional under which bounded Palais-Smale sequences are convergent. Finally, we make some comment concerning the convergence of Palais-Smale sequence obtained in the mountain pass theorem due to Rabier.
Details
- Language :
- English
- ISSN :
- 21919496, 2191950X, and 20200102
- Volume :
- 10
- Issue :
- 1
- Database :
- Directory of Open Access Journals
- Journal :
- Advances in Nonlinear Analysis
- Publication Type :
- Academic Journal
- Accession number :
- edsdoj.275b5927044cd087478445300012ed
- Document Type :
- article
- Full Text :
- https://doi.org/10.1515/anona-2020-0102