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Description:
This paper considers a pair of coupled nonlinear Helmholtz equations on R$^{n}$ where $\frac{2(N+1)}{N−1}$ < $p$ < 2$^{*}$. The existence of nontrivial strong solutions in W$^{2,p}$(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.