An Introduction to Nonlinear Analysis: Applications

Denkowski, Zdzisław; Migórski, Stanisław; Papageorgiou, Nikolas S.

doi:10.1007/978-1-4419-9156-0

Cited by 214 publications

(286 citation statements)

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“…23.4 of [32], Chap. 3.4 of [7]). Moreover, for 0 < T < ∞, we introduce the following spaces V = L 2 (0, T ; V ) and W = {v ∈ V|v ∈ V * }.…”

Section: Lemma 5 Let X Be a Banach Space With A Normmentioning

confidence: 96%

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A Dynamic Contact Problem with History-Dependent Operators

Ogorzaly

2016

J Elast

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In this paper we present results on existence, uniqueness and convergence of solutions to the Cauchy problem for abstract first order evolutionary inclusion which contains two operators depending on the history of the solution. These results are applicable to a dynamic contact problem for viscoelastic materials with a normal compliance contact condition with memory and a friction law in which the friction bound depends on the magnitude of the tangential displacement. The proofs are based on recent results for hemivariational inequalities and a fixed point argument.

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“…23.4 of [32], Chap. 3.4 of [7]). Moreover, for 0 < T < ∞, we introduce the following spaces V = L 2 (0, T ; V ) and W = {v ∈ V|v ∈ V * }.…”

Section: Lemma 5 Let X Be a Banach Space With A Normmentioning

confidence: 96%

“…In the paper we use the concepts of the generalized directional derivative and the Clarke subdifferential, see, for example, [6,7] and [21].…”

Section: Preliminariesmentioning

confidence: 99%

A Dynamic Contact Problem with History-Dependent Operators

Ogorzaly

2016

J Elast

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“…We start with a basic notation and preliminary results on the abstract history-dependent subdifferential inclusions. For additional details on the material presented in this section we refer to [3][4][5][13][14][15]17].…”

Section: History-dependent Subdifferential Inclusionsmentioning

confidence: 99%

“…We show that F(t, ·) is pseudomonotone (cf. Definition 6.3.63 of [5]) and coercive for a.e. fixed t ∈ (0, T ).…”

Section: Lemmamentioning

confidence: 99%

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History-Dependent Problems with Applications to Contact Models for Elastic Beams

et al. 2015

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We prove an existence and uniqueness result for a class of subdifferential inclusions which involve a history-dependent operator. Then we specialize this result in the study of a class of history-dependent hemivariational inequalities. Problems of such kind arise in a large number of mathematical models which describe quasistatic processes of contact. To provide an example we consider an elastic beam in contact with a reactive obstacle. The contact is modeled with a new and nonstandard condition which involves both the subdifferential of a nonconvex and nonsmooth function and a Volterra-type integral term. We derive a variational formulation of the problem which is in the form of a history-dependent hemivariational inequality for the displacement field. Then, we use our abstract result to prove its unique weak solvability. Finally, we consider a numerical approximation of the model, solve effectively the approximate problems and provide numerical simulations.

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Positive solutions and multiple solutions for periodic problems driven by scalar p ‐Laplacian

Papageorgiou

2006

Mathematische Nachrichten

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In this paper we study a nonlinear second order periodic problem driven by a scalar p-Laplacian and with a nonsmooth, locally Lipschitz potential function. Using a variational approach based on the nonsmooth critical point theory for locally Lipschitz functions, we first prove the existence of nontrivial positive solutions and then establish the existence of a second distinct solution (multiplicity theorem) by strengthening further the hypotheses.

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An Introduction to Nonlinear Analysis: Applications

Cited by 214 publications

References 0 publications

A Dynamic Contact Problem with History-Dependent Operators

A Dynamic Contact Problem with History-Dependent Operators

History-Dependent Problems with Applications to Contact Models for Elastic Beams

Positive solutions and multiple solutions for periodic problems driven by scalar p ‐Laplacian

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