Views
3 years ago

a version of zhong's coercivity result for a general class of ...

a version of zhong's coercivity result for a general class of ...

a version of zhong's coercivity result for a general class of

A VERSION OF ZHONG’S COERCIVITY RESULTFOR A GENERAL CLASS OF NONSMOOTHFUNCTIONALSD. MOTREANU, V. V. MOTREANU, AND D. PAŞCAReceived 27 October 2001A version of Zhong’s coercivity result (1997) is established for nonsmooth functionalsexpressed as a sum Φ + Ψ, whereΦ is locally Lipschitz and Ψ is convex,lower semicontinuous, and proper. This is obtained as a consequence of ageneral result describing the asymptotic behavior of the functions verifying theabove structure hypothesis. Our approach relies on a version of Ekeland’s variationalprinciple. In proving our coercivity result we make use of a new generalPalais-Smale condition. The relationship with other results is discussed.1. IntroductionIn this paper, we deal with the class of nonsmooth functionals I : X → R ∪{+∞}on a Banach space X of the formI = Φ + Ψ, (1.1)with Φ : X → R locally Lipschitz and Ψ : X → R ∪{+∞} convex, lower semicontinuous(l.s.c.), and proper (i.e., ≢ +∞).For the functional I as in (1.1), it was given in [9] the following definition ofPalais-Smale (PS) condition.Definition 1.1. The functional I : X → R ∪{+∞} in (1.1) satisfies the PS conditionif every sequence (u n ) ⊂ X with I(u n ) bounded and for which there exists asequence (ɛ n ) ⊂ R + , ɛ n → 0 + ,suchthatΦ 0( u n ;v − u n) + Ψ(v) − Ψ(un)≥−ɛn∥ ∥ v − u n∥ ∥ , ∀v ∈ X, ∀n, (1.2)contains a (strongly) convergent subsequence in X.Copyright © 2002 Hindawi Publishing CorporationAbstract and Applied Analysis 7:11 (2002) 601–6122000 Mathematics Subject Classification: 58E30, 58E05, 49K27URL: http://dx.doi.org/10.1155/S1085337502207058

Almost metric versions of Zhong's variational principle
generalization of some results to quasi-metric spaces and its ...
Regularity Results for a Class of Functionals - Trends in the ...
Results by Class (generic) - Performance Timing, LLC
Results _ generic by class _.rtf - Performance Timing, LLC
Results by Class (generic) - Performance Timing, LLC
Results by Class (generic) - Performance Timing, LLC
Results by Class (generic) - Performance Timing, LLC
Results by Class (generic) - Performance Timing, LLC
Groups Generated by Class Transpositions – Results and ... - Gap
Results by Class (generic) - Performance Timing, LLC
Results by Class (generic) - The Utah Nordic Alliance
Results by Class (generic) - Performance Timing, LLC
ON A GENERAL CLASS OF LINEAR AND POSITIVE OPERATORS
Results by Class (generic) - Performance Timing, LLC
Subordination results for certain classes of analytic functions defined ...
Results by Class (generic) - Performance Timing, LLC
A generalized class of starlike functions associated with the Wright ...
A class of multivalent harmonic functions involving a generalized ...
A MULTIPLICITY RESULT FOR A CLASS OF ... - Ngô Quốc Anh
Weak Convergence Results for Multiple Generations of a Branching ...
Generalized Variational Inequalities - Heldermann-Verlag
Subordination results for certain classes of analytic functions defined ...
chicago bears generate first class results - Odds On Promotions
A generalized class of starlike functions associated with the Wright ...
88 ON q-LAPLACE TRANSFORMS OF A GENERAL CLASS OF q ...
Fixed point results for contractions involving generalized ... - Springer
Weighted Generating Functions and Configuration Results for Type ...