Bifurcations of elliptic systems with linear couplings

Consider the elliptic system with linearly coupled terms {-Delta u = lambda v + f(1)(u, v), in Omega, -Delta v = mu u + f(2)(u, v), in Omega, u = 0, v = 0, on partial derivative Omega, where lambda,mu is an element of R are constants and Omega subset of R-N is a smooth bounded domain. We study the local and global bifurcations with respect to T-0 := {((lambda, mu), (0, 0))} subset of R-2 x X, where X is a proper Banach space. Our results are of particular interest for obtaining nontrivial solutions in the case lambda not equal mu. (C) 2019 Elsevier Ltd. All rights reserved.