Abstract
We study the Schrödinger systems with linear and nonlinear coupling terms (doubly coupled nonlinear Schrödinger system for short) which arise naturally in nonlinear optics, and in the Hartree–Fock theory for Bose–Einstein condensates, among other physical problems. First, for small linear coupling constant, we get existence of a nontrivial bound state solution to the system via perturbation method, furthermore, we prove each component of the bound state solution is nonnegative by energy estimate. Second, we establish a version of Pohozaev–Nehari identity and prove a nonexistence result for the more general system when the spatial dimension N ≥ 4 .
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