Entire solutions of schrödinger elliptic systems with discontinuous nonlinearity and sign‐changing potential¹

This paper is dedicated to the memory of my father, Tudor Dinu.

Abstract

We establish the existence of an entire solution for a class of stationary Schrodinger systems with subcritical discontinuous nonlinearities and lower bounded potentials that blow‐up at infinity. The proof is based on the critical point theory in the sense of Clarke and we apply the Mountain Pass Lemma for locally Lipschitz functionals. Our result generalizes in a nonsmooth framework the result of Rabinowitz [16] on the existence of entire solutions of the nonlinear Schrodinger equation.

Key words:

• nonlinear elliptic system
• entire solution
• Lipschitz functional
• Clarke generalized gradient

Notes

This paper is dedicated to the memory of my father, Tudor Dinu.