Behaviour of symmetric solutions of a nonlinear elliptic field equation in the semi-classical limit: Concentration around a circle.
Locating the boundary peaks of least-energy solutions to a singularly perturbed Dirichlet problem
We consider the problemwhere is a smooth and bounded domain, , . We prove that this system has a which develops, as , a single spike layer located near the boundary, in striking contrast with the result in [37] for the single Schrödinger equation. Moreover the unique peak approaches thepart of ,, where the boundary mean curvature assumes its maximum. Thus this elliptic system, even though it is a Dirichlet problem, acts more like a Neumann problem for the...
Clustered solutions around harmonic centers to a coupled elliptic system
Existence, multiplicity and profile of sign-changing clustered solutions of a semiclassical nonlinear Schrödinger equation
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