Semiclassical States of Nonlinear Schrödinger Equations

The existence of semiclassical states to some nonlinear Schr?dinger equations that concentrate near the critical points of the potential V is studied by means of a local approach, variational in nature. We also discuss stability and necessary conditions for concentration. The same method is used to find multiple homoclinic orbits to a class of second‐order Hamiltonian systems. (Accepted April 24, 1996)