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Approximation of abstract linear integrodifferential equations

100%
Oka H., Tanaka N.
Studia Mathematica
|
2000
|
tom 140
|
nr 1
1-14
EN
This paper is devoted to the approximation of abstract linear integrodifferential equations by finite difference equations. The result obtained here is applied to the problem of convergence of the backward Euler type discrete scheme.
2
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Controllability for some partial functional integrodifferential equations with nonlocal conditions in Banach spaces

100%
Ezzinbi K., Degla G., Ndambomve P.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
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2015
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tom 35
|
nr 1
25-46
EN
This work concerns the study of the controllability of some partial functional integrodifferential equation with nonlocal initial conditions in Banach spaces. It gives sufficient conditions that ensure the controllability of the system by supposing that its linear homogeneous part admits a resolvent operator in the sense of Grimmer, and by making use of the measure of noncompactness and the Mönch fixed-point theorem. As a result, we obtain a generalization of the work of Y.K. Chang, J.J. Nieto and W.S. Li (J. Optim. Theory Appl. 142, 267-273 (2009)), without assuming the compactness of the resolvent operator. An example of application is given for illustration.
3
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Quasilinear vector differential equations with maximal monotone terms and nonlinear boundary conditions

72%
Bader R., Papageorgiou N. S.
Annales Polonici Mathematici
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2000
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tom 73
|
nr 1
69-92
EN
We consider a quasilinear vector differential equation which involves the p-Laplacian and a maximal monotone map. The boundary conditions are nonlinear and are determined by a generally multivalued, maximal monotone map. We prove two existence theorems. The first assumes that the maximal monotone map involved is everywhere defined and in the second we drop this requirement at the expense of strengthening the growth hypothesis on the vector field. The proofs are based on the theory of operators of monotone type and on the Leray-Schauder fixed point theorem. At the end we present some special cases (including the classical Dirichlet, Neumann and periodic problems), which illustrate the general and unifying features of our work.
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