Real Analysis Exchange

Variational Methods in the Study of Inequality Problems for Nonlinear Elliptic Systems with Lack of Compactness

Teodora-Liliana Dinu

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Abstract

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 Rabinowitz [12] related to entire solutions of the Schrödinger equation.

Article information

Source
Real Anal. Exchange, Volume 33, Number 1 (2007), 1-14.

Dates
First available in Project Euclid: 28 April 2008

Permanent link to this document
https://projecteuclid.org/euclid.rae/1209398373

Mathematical Reviews number (MathSciNet)
MR2402858

Zentralblatt MATH identifier
1141.35053

Subjects
Primary: 35J50: Variational methods for elliptic systems 49J52: Nonsmooth analysis [See also 46G05, 58C50, 90C56] 58E05: Abstract critical point theory (Morse theory, Ljusternik-Schnirelman (Lyusternik-Shnirel m an) theory, etc.)

Keywords
nonlinear elliptic system entire solution Lipschitz functional Clarke generalized gradient

Citation

Dinu, Teodora-Liliana. Variational Methods in the Study of Inequality Problems for Nonlinear Elliptic Systems with Lack of Compactness. Real Anal. Exchange 33 (2007), no. 1, 1--14. https://projecteuclid.org/euclid.rae/1209398373


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