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Zbl 1156.35360
Eden, A.; Erbay, S.
Standing waves for a generalized Davey--Stewartson system. (English)
[J] J. Phys. A, Math. Gen. 39, No. 43, 13435-13444 (2006). ISSN 0305-4470

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 2000:
*35J60 Nonlinear elliptic equations
35J20 Second order elliptic equations, variational methods
35Q55 NLS-like (nonlinear Schroedinger) equations

Keywords: semilinear elliptic equation; Davey-Stewartson system; standing wave solutions

Cited in: Zbl 1165.35458

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