Special Session 35: Elliptic PDEs: singularities, discontinuities, and nonlinear phenomena

Multiplicity of mountain-pass type transition solutions for Lagrangian systems with double-well potentials
Piero Montecchiari
Universita` Politecnica delle Marche
Italy
Co-Author(s):    
Abstract:
We present several results concerning the multiplicity of heteroclinic and homoclinic solutions of mountain-pass type for non-autonomous Lagrangian systems of Allen-Cahn type. In particular, we show that, under natural non-degeneracy assumptions, multi-transition local minimizers generate distinct local mountain-pass structures, giving rise to multiple associated mountain-pass type solutions.