Existence of nonzero weak solutions for a class of elliptic variational inclusions systems in RN

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8 Citations (Scopus)

Abstract

We consider the following variational inclusions system of the form- △ u + u ∈ ∂1 F (u, v) in RN,- △ v + v ∈ ∂2 F (u, v) in RN, with u, v ∈ H1 (RN), where F : R2 → R is a locally Lipschitz function and ∂i F (u, v) (i ∈ {1, 2}) are the partial generalized gradients in the sense of Clarke. Under various growth conditions on the nonlinearity F we study the existence of nonzero weak solutions of the above system (in the sense of hemivariational inequalities), which are critical points of an appropriate locally Lipschitz function defined on H1 (RN) × H1 (RN). The main tool used in the paper is the principle of symmetric criticality for locally Lipschitz functions.

Original languageEnglish
Pages (from-to)1578-1594
Number of pages17
JournalNonlinear Analysis
Volume65
Issue number8
DOIs
Publication statusPublished - okt. 15 2006

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Locally Lipschitz Function
Variational Inclusions
Weak Solution
Hemivariational Inequality
Generalized Gradient
Criticality
Growth Conditions
Critical point
Nonlinearity
Partial
Class

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics
  • Mathematics(all)

Cite this

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title = "Existence of nonzero weak solutions for a class of elliptic variational inclusions systems in RN",
abstract = "We consider the following variational inclusions system of the form- △ u + u ∈ ∂1 F (u, v) in RN,- △ v + v ∈ ∂2 F (u, v) in RN, with u, v ∈ H1 (RN), where F : R2 → R is a locally Lipschitz function and ∂i F (u, v) (i ∈ {1, 2}) are the partial generalized gradients in the sense of Clarke. Under various growth conditions on the nonlinearity F we study the existence of nonzero weak solutions of the above system (in the sense of hemivariational inequalities), which are critical points of an appropriate locally Lipschitz function defined on H1 (RN) × H1 (RN). The main tool used in the paper is the principle of symmetric criticality for locally Lipschitz functions.",
keywords = "Cerami condition, Hemivariational inequalities, Locally Lipschitz functions, Palais-Smale condition, Principle of symmetric criticality, Variational inclusions system",
author = "A. Krist{\'a}ly",
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TY - JOUR

T1 - Existence of nonzero weak solutions for a class of elliptic variational inclusions systems in RN

AU - Kristály, A.

PY - 2006/10/15

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N2 - We consider the following variational inclusions system of the form- △ u + u ∈ ∂1 F (u, v) in RN,- △ v + v ∈ ∂2 F (u, v) in RN, with u, v ∈ H1 (RN), where F : R2 → R is a locally Lipschitz function and ∂i F (u, v) (i ∈ {1, 2}) are the partial generalized gradients in the sense of Clarke. Under various growth conditions on the nonlinearity F we study the existence of nonzero weak solutions of the above system (in the sense of hemivariational inequalities), which are critical points of an appropriate locally Lipschitz function defined on H1 (RN) × H1 (RN). The main tool used in the paper is the principle of symmetric criticality for locally Lipschitz functions.

AB - We consider the following variational inclusions system of the form- △ u + u ∈ ∂1 F (u, v) in RN,- △ v + v ∈ ∂2 F (u, v) in RN, with u, v ∈ H1 (RN), where F : R2 → R is a locally Lipschitz function and ∂i F (u, v) (i ∈ {1, 2}) are the partial generalized gradients in the sense of Clarke. Under various growth conditions on the nonlinearity F we study the existence of nonzero weak solutions of the above system (in the sense of hemivariational inequalities), which are critical points of an appropriate locally Lipschitz function defined on H1 (RN) × H1 (RN). The main tool used in the paper is the principle of symmetric criticality for locally Lipschitz functions.

KW - Cerami condition

KW - Hemivariational inequalities

KW - Locally Lipschitz functions

KW - Palais-Smale condition

KW - Principle of symmetric criticality

KW - Variational inclusions system

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JO - Nonlinear Analysis, Theory, Methods and Applications

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SN - 0362-546X

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