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Standing waves for a generalized Davey–Stewartson system. (English) Zbl 1156.35360
Summary: We establish the existence of non-trivial solutions for a semi-linear elliptic partial differential equation with a non-local term. This result allows us to prove the existence of standing wave (ground state) solutions for a generalized Davey–Stewartson system. A sharp upper bound is also obtained on the size of the initial values for which solutions exist globally.

MSC:
35J60Nonlinear elliptic equations
35J20Second order elliptic equations, variational methods
35Q55NLS-like (nonlinear Schrödinger) equations