Abstract
We prove the monotonicity and one-dimensional symmetry of solutions to non-cooperative elliptic systems in RN with uniform limits under mild assumptions on the nonlinearities. These problems arise in the study of domain walls and interface layers of two-component Bose–Einstein condensates in the segregation regime. We also derive analogous results for systems in half-spaces and strips. We introduce a variant of the sliding method for non-cooperative elliptic systems to prove our results.
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