Problèmes globaux dans le théorie des équations intégrales de Volterra

Corduneanu, C.

doi:10.1007/bf02410815

Cited by 68 publications

(35 citation statements)

References 4 publications

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“…Other authors (for example [12] and [13]) have approached the problem by continuing local solutions obtained by iteration, or by employing topological methods for existence and then imposing further restrictions to obtain uniqueness. Corduneanu, [2], has obtained direct global results (not including ours) with an eye to stability theorems by employing methods that bear some similarity to those of our example. Now, suppose A is any absolutely convex and bounded set in C. We may regard H as a mapping of (CA x R) x C -> C, where CA is given its norm topology under || • \\A.…”

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confidence: 75%

Implicitly defined mappings in locally convex spaces

McDermott¹

1971

Trans. Amer. Math. Soc.

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Abstract. Results on existence, uniqueness, continuity and differentiability of implicit functions in locally convex, linear topological spaces are obtained, and certain of these results are applied to obtain results on the existence and continuous dependence on parameters of global solutions for a nonlinear Volterra integral equation. In this article, we discuss the problem of implicit functions in locally convex spaces in light of the ideas and results developed in [11]. In §1 we give conditions for the existence of an implicit function, then obtain results dealing with its uniqueness and continuity. In §2 certain results from the first are applied to discuss global, continuous solutions for a nonlinear, Volterra integral equation. Finally, in §3 we give conditions under which a differentiable implicit function will exist, differentiability being understood in the sense of Sebastiào è Silva [14].For the convenience of the reader, §0 has been included containing the essential definitions and results from [11] that are used in the present work.

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confidence: 75%

Implicitly defined mappings in locally convex spaces

McDermott¹

1971

Trans. Amer. Math. Soc.

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“…as a complete metric space in which the corresponding topology is induced by a countable family of seminorms. Details can be found in [11] and [24], for instance. Here we restrict ourselves to recall that the convergence of a sequence (x k ) k to the element x, in the space C(R + ; X), can be described as follows:…”

Section: Notation and Preliminariesmentioning

confidence: 99%

Analysis of a contact problem with normal damped response and unilateral constraint

Barboteu

Danan

Sofonea

2015

Z. Angew. Math. Mech.

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We consider a mathematical model which describes the equilibrium of a viscoelastic body in frictional contact with an obstacle. The contact is modeled with normal damped response and unilateral constraint for the velocity field, associated to a version of Coulomb's law of dry friction. We present a weak formulation of the problem, then we state and prove an existence and uniqueness result of the solution. The proof is based on arguments of history-dependent quasivariational inequalities. We also study the dependence of the solution with respect to the data and prove a convergence result. Further, we introduce a fully discrete scheme to solve the problem numerically. Under certain solution regularity assumptions, we derive an optimal order error estimate of the discretization. Finally, we provide numerical simulations which illustrate the behavior of the solution with respect to the frictional contact conditions and validate the theoretical convergence results.

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“…In another direction, it was pointed out interest in the asymptotic behavior of solutions for integral equations, too; for the Volterra equations, the fundamental paper of C. Corduneanu [10] and for the Hammerstein equation the one of D. Petrovanu [21]. The existence problem of convergent solutions for the integral equations has been considered in [4,5,6].…”

Section: = F (T X) X(a) = X(b) (14)mentioning

confidence: 99%

“…The admissibility with respect to an integral operator has been considered first by C. Corduneanu [10] and D. Petrovanu [21]. The admissibility hypothesis on the pair (C l , C l ) is developed in [4].…”

Section: 5mentioning

confidence: 99%