Abstract
This paper considers a pair of coupled nonlinear Helmholtz equations
on \(\mathbb {R}^N\) where \(\frac{2(N+1)}{N-1}< p < 2^*\). The existence of nontrivial strong solutions in \(W^{2, p}(\mathbb {R}^N)\) is established using dual variational methods. The focus lies on necessary and sufficient conditions on the parameters deciding whether or not both components of such solutions are nontrivial.
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Mandel, R., Scheider, D. Dual variational methods for a nonlinear Helmholtz system. Nonlinear Differ. Equ. Appl. 25, 13 (2018). https://doi.org/10.1007/s00030-018-0504-z
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DOI: https://doi.org/10.1007/s00030-018-0504-z