A multiplicity result for hemivariational inequalities

Faraci, Francesca; Iannizzotto, Antonio; Lisei, Hannelore; Varga, Csaba

doi:10.1016/j.jmaa.2006.07.081

Cited by 4 publications

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“…the monographs [14,16,17,[24][25][26]29,32,33]) as it allowed mathematical formulations for new classes of interesting problems (see e.g. [1,[6][7][8]11,12,[19][20][21][22]). …”

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Inequality problems of quasi-hemivariational type involving set-valued operators and a nonlinear term

Costea

Rădulescu

2011

J Glob Optim

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The aim of this paper is to establish the existence of at least one solution for a general inequality of quasi-hemivariational type, whose solution is sought in a subset K of a real Banach space E. First, we prove the existence of solutions in the case of compact convex subsets and the case of bounded closed and convex subsets. Finally, the case when K is the whole space is analyzed and necessary and sufficient conditions for the existence of solutions are stated. Our proofs rely essentially on the Schauder's fixed point theorem and a version of the KKM principle due to Ky Fan (Math Ann 266: [519][520][521][522][523][524][525][526][527][528][529][530][531][532][533][534][535][536][537] 1984).Keywords Quasi-hemivariational inequality · Set-valued operator · Lower semicontinuous set-valued operator · Clarke's generalized gradient · Generalized monotonicity · KKM mapping Mathematics Subject Classification (2000) 47J20 · 47H04 · 49J53 · 54C60 · 47H05 Introduction and preliminariesThe study of inequality problems captured special attention in the last decades, one of the most recent and general type of inequalities being the hemivariational inequalities. The notion of hemivariational inequality was introduced by P.D. Panagiotopoulos at the beginning of the 1980s (see e.g. [27,28]) as a variational formulation for several classes of mechanical problems with nonsmooth and nonconvex energy super-potentials. In the case of convex super-potentials, hemivariational inequalities reduce to variational inequalities which were studied earlier by many authors (see e.g. Fichera [13] or Hartman and Stampacchia [18]).

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“…the monographs [14,16,17,[24][25][26]29,32,33]) as it allowed mathematical formulations for new classes of interesting problems (see e.g. [1,[6][7][8]11,12,[19][20][21][22]). …”

mentioning

confidence: 99%

Inequality problems of quasi-hemivariational type involving set-valued operators and a nonlinear term

Costea

Rădulescu

2011

J Glob Optim

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“…The study of hemivariational inequalities by using critical point theory for nonsmooth functionals on unbounded domains started with the work of Gazzola and Rȃdulescu [8], followed by papers dealing with multiplicity results such as the papers of Kristály [11,12], Dályai and Varga [5], Varga [21], Faraci, Iannizzotto, Lisei and Varga [6]. A survey paper about hemivariational and variational-hemivariational inequalities defined on unbounded domains is [13] written by A.…”

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confidence: 99%