Quasilinear asymptotically linear Schrödinger problem in R^N without monotonicity
Date
2018-09-11
Authors
Miyagaki, Olimpio H.
Moreira, Sandra I.
Ruviaro, Ricardo
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
We establish existence and non-existence results for a quasilinear asymptotically linear Schrodinger problem. In the first result, we prove that a minimization problem constrained to the Pohozaev manifold is not achieved. In the second, the main argument consists in a splitting lemma for a functional constrained to the Pohozaev manifold. Because of the lack of the monotonicity we are not able to project to the usual Nehari manifold any longer, and this approach is crucial in order to compare the critical level to reach a contradiction. This argument was used in [21, 24, 32] for semilinear equations and in [11] for quasilinear equations.
Description
Keywords
Quasilinear Schrödinger equations, Variational methods, Asymptotically linear
Citation
Miyagaki, O. H., Moreira, S. I., & Ruviaro, R. (2018). Quasilinear asymptotically linear Schrödinger problem in R^N without monotonicity. <i>Electronic Journal of Differential Equations, 2018</i>(164), pp. 1-21.
Rights
Attribution 4.0 International