Classification of Ground-states of a coupled Schrodinger system

摘要

The paper is concerned with the existence of nontrivial ground-state solutions for a coupled nonlinear Schrodinger system @@@ {-Delta u(j) + lambda u(j) = mu vertical bar u(j)vertical bar(2p) u(j) + Sigma(m)(i not equal j) beta vertical bar u(i)vertical bar(p+1)vertical bar u(j)vertical bar(p-1) u(j), in R-n, @@@ u(j)(x)-> 0 as vertical bar x vertical bar -> infinity, j = 1,2,...,m, @@@ where m >= 2, 0 < p < 2/(n-2)(+), lambda > 0, mu > 0 and beta > 0. We establish a sufficient and necessary condition for the existence of nontrivial ground-state solutions which have the least energy among all the non-zero solutions of the system and whose components have the same modulus. This gives an affirmative answer to a conjecture raised in Correia (Nonlinear Anal. 140:112-129, 2016).

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