6533b861fe1ef96bd12c4f51

RESEARCH PRODUCT

Bounded Palais–Smale sequences for non-differentiable functions

Dumitru MotreanuPasquale CanditoRoberto Livrea

subject

Lemma (mathematics)Pure mathematicsApplied MathematicsMathematical analysisNon-smooth functionsFunction (mathematics)Lipschitz continuityMeasure (mathematics)Infimum and supremumDeformationCritical pointBounded Palais-Smale sequenceBounded functionMountain pass geometryDifferentiable functionConvex functionAnalysisMathematics

description

The existence of bounded Palais-Smale sequences (briefly BPS) for functionals depending on a parameter belonging to a real interval and which are the sum of a locally Lipschitz continuous term and of a convex, proper, lower semicontinuous function, is obtained when the parameter runs in a full measure subset of the given interval. Specifically, for this class of non-smooth functions, we obtain BPS related to mountain pass and to global infima levels. This is done by developing a unifying approach, which applies to both cases and relies on a suitable deformation lemma. © 2011 Elsevier Ltd. All rights reserved.

yearjournalcountryeditionlanguage
2011-11-01Nonlinear Analysis: Theory, Methods & Applications
https://doi.org/10.1016/j.na.2011.05.030