Journal
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS
Volume 31, Issue -, Pages 473-491Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.nonrwa.2016.03.004
Keywords
Schrodinger-Maxwell system; Riemannian manifold; Non-compact; Isometry; Existence; Multiplicity
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Funding
- Romanian National Authority for Scientific Research, Symmetries in elliptic problems: Euclidean and non-Euclidean techniques, CNCS-UEFISCDI [PN-II-ID-PCE-2011-3-0241]
- Janos Bolyai Research Scholarship of the Hungarian Academy of Sciences
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In this paper we study nonlinear Schrodinger-Maxwell systems on n-dimensional non-compact Riemannian manifolds of Hadamard type, 3 <= n <= 5. The main difficulty resides in the lack of compactness which is recovered by exploring suitable isometric actions of the Hadamard manifolds. By combining variational arguments, some existence, uniqueness and multiplicity of isometry-invariant weak solutions are established for the Schrodinger-Maxwell system depending on the behavior of the nonlinear term. (C) 2016 Elsevier Ltd. All rights reserved.
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