Existence and Nonexistence of Entire Solutions for Non-cooperative Cubic Elliptic Systems
نویسنده
چکیده
In this paper we deal with the cubic Schrödinger system −∆ui = n ∑ j=1 βiju 2 jui, u1, . . . , un ≥ 0 in R N (N ≤ 3), where β = (βi,j)ij is a symmetric matrix with real coefficients and βii ≥ 0 for every i = 1, . . . , n. We analyse the existence and nonexistence of nontrivial solutions in connection with the properties of the matrix β, and provide a complete characterization in dimensions N = 1, 2. Extensions to more general power-type nonlinearities are given.
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تاریخ انتشار 2010