Physical Sciences and Mathematics Commons^™

We consider a singularly perturbed elliptic PDE that arises in the study of nonlinear Schrodinger equations. We seek solutions that are positive on the entirety of Euclidean space and that vanish at infinity. Under the assumption that the nonlinear term of the PDE satisfies super-linear and sub-critical growth conditions, we show that for small values of the epsilon parameter in the PDE, there solutions that concentrate near local minima of V (a coefficient function in the PDE) . The local minima may occur in unbounded components, as long as the Laplacian of V achieves a strict local minimum along such …