Variational methods in the study of inequality problems for nonlinear elliptic systems with lack of compactness. (English) Zbl 1141.35053

Dinu, Teodora-Liliana

Real Anal. Exch. 33(2007-2008), No. 1, 1-14 (2008).

Summary: We establish the existence of an entire weak solution for a class of stationary Schrödinger systems with subcritical discontinuous nonlinearities and lower bounded potentials that blow-up at infinity. The proof relies on Chang’s version of the mountain pass lemma for locally Lipschitz functionals. Our result generalizes in a nonsmooth framework, a result of P. H. Rabinowitz [Z. Angew. Math. Phys. 43, No. 2, 270–291 (1992; Zbl 0763.35087)] related to entire solutions of the Schrödinger equation.

MSC:

35Q55	NLS equations (nonlinear Schrödinger equations)
35J50	Variational methods for elliptic systems
49J52	Nonsmooth analysis
58E05	Abstract critical point theory (Morse theory, Lyusternik-Shnirel’man theory, etc.) in infinite-dimensional spaces

Keywords:

nonlinear elliptic system; entire solution; Lipschitz functional; Clarke generalized gradient; Schrödinger equation; mountain pass lemma

Citations:

Zbl 0763.35087