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.