Non-smooth critical point theory on closed convex sets

Salvatore A. Marano; Sunra Mosconi

doi:10.3934/cpaa.2014.13.1187

Article Contents

2014, Volume 13, Issue 3: 1187-1202. Doi: 10.3934/cpaa.2014.13.1187

This issue Previous Article The lifespan for quasilinear wave equations with multiple propagation speeds in four space dimensions Next Article Global existence and pointwise estimates of solutions for the multidimensional generalized Boussinesq-type equation

Non-smooth critical point theory on closed convex sets

Salvatore A. Marano^1, and
Sunra Mosconi^1,

1.
Dipartimento di Matematica e Informatica, Università degli Studi di Catania, Viale A. Doria 6, 95125 Catania

Received: April 30, 2013

Revised: August 31, 2013

Published: April 2015

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Abstract

A critical point theory for non-differentiable functionals defined on a closed convex subset of a Banach space is worked out. Special attention is paid to the notion of critical point and possible compactness conditions of Palais-Smale's type. Two Mountain-Pass like theorems are also established. Concepts and results are compared with those already existing in the literature.

Keywords:

Critical point,
weak Palais-Smale condition,
min-max theorem,
functional defined on a closed convex set,
non-smooth function.

Mathematics Subject Classification: Primary: 58E05, 49J35; Secondary: 49J52.

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