Existence of normalized solutions for semilinear elliptic systems with potential

摘要

In this paper, we consider the existence of normalized solutions to the following system: -Delta u + V-1(x)u + lambda u = mu(1)u(3) + beta v(2)u and -Delta v + V-2(x)v + lambda v = mu(2)v(3) + beta u(2)v in R-3, under the mass constraint integral(R3)u(2) + v(2) = rho(2), where rho is prescribed, mu(i), beta > 0 (i = 1, 2), and lambda is an element of R appears as a Lagrange multiplier. Then, by a min-max argument, we show the existence of fully nontrivial normalized solutions under various conditions on the potential V-i:R-3 -> R(i=1,2). Published under an exclusive license by AIP Publishing.

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