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1
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A sufficient condition for the existence of multiple periodic solutions of differential inclusions

100%
Bader R.
Banach Center Publications
|
1996
|
tom 35
|
nr 1
129-138
2
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Nonlinear multivalued boundary value problems

63%
Bader R., Papageorgiou N.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
|
2001
|
tom 21
|
nr 1
127-148
EN
In this paper, we study nonlinear second order differential inclusions with a multivalued maximal monotone term and nonlinear boundary conditions. We prove existence theorems for both the convex and nonconvex problems, when $domA ≠ ℝ^{N}$ and $domA = ℝ^{N}$, with A being the maximal monotone term. Our formulation incorporates as special cases the Dirichlet, Neumann and periodic problems. Our tools come from multivalued analysis and the theory of nonlinear monotone operators.
3
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Quasilinear vector differential equations with maximal monotone terms and nonlinear boundary conditions

63%
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.
4
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On the topological dimension of the solutions sets for some classes of operator and differential inclusions

51%
Bader R., Gel'man B., Kamenskii M., Obukhovskii V.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
|
2002
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tom 22
|
nr 1
17-32
EN
In the present paper, we give the lower estimation for the topological dimension of the fixed points set of a condensing continuous multimap in a Banach space. The abstract result is applied to the fixed point set of the multioperator of the form $𝓕 = S 𝓟_F$ where $𝓟_F$ is the superposition multioperator generated by the Carathéodory type multifunction F and S is the shift of a linear injective operator. We present sufficient conditions under which this set has the infinite topological dimension. In the last section of the paper, we consider the applications of the solutions sets for Cauchy and periodic problems for semilinear differential inclusions in a Banach space.
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