High frequency solutions for singularly perturbed elliptic problems

Salome Martinez
Universidad de Chile
Centro de Modelamiento Matematico
email: samartin@dim.uchile.cl

Abstract: In this talk we will characterize high frequency solutions for some singularly perturbed elliptic semilinear examples. In particular, we will construct solutions of the singularly perturbed nonlinear Schr\"odinger equation in 1 dimension which oscillate in intervals, and also we will give results for the radial case, providing changing sign solutions that concentrate in a ball centered at the origin and positive solutions concentrating in an annulus. We will also show how our methods can be applied to the constructions of solutions for Gierer-Meinhardt system in which the activator exhibits highly oscillatory behavior.