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Discontinuous quasilinear elliptic problems at resonance

100%
Kourogenis N. C., Papageorgiou N. S.
Colloquium Mathematicum
|
1998
|
tom 78
|
nr 2
213-223
EN
In this paper we study a quasilinear resonant problem with discontinuous right hand side. To develop an existence theory we pass to a multivalued version of the problem, by filling in the gaps at the discontinuity points. We prove the existence of a nontrivial solution using a variational approach based on the critical point theory of nonsmooth locally Lipschitz functionals.
2
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Quasilinear vector differential equations with maximal monotone terms and nonlinear boundary conditions

100%
Bader R., Papageorgiou N. S.
Annales Polonici Mathematici
|
2000
|
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.
3
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Existence and multiplicity results for nonlinear eigenvalue problems with discontinuities

100%
Papageorgiou N. S., Papalini F.
Annales Polonici Mathematici
|
2000
|
tom 75
|
nr 2
125-141
EN
We study eigenvalue problems with discontinuous terms. In particular we consider two problems: a nonlinear problem and a semilinear problem for elliptic equations. In order to study the existence of solutions we replace these two problems with their multivalued approximations and, for the first problem, we estabilish an existence result while for the second problem we prove the existence of multiple nontrivial solutions. The approach used is variational.
4
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Multiple solutions for nonlinear discontinuous elliptic problems near resonance

100%
Kourogenis N. C., Papageorgiou N. S.
Colloquium Mathematicum
|
1999
|
tom 81
|
nr 1
89-99
EN
We consider a quasilinear elliptic eigenvalue problem with a discontinuous right hand side. To be able to have an existence theory, we pass to a multivalued problem (elliptic inclusion). Using a variational approach based on the critical point theory for locally Lipschitz functions, we show that we have at least three nontrivial solutions when $λ → λ_1$ from the left, $λ_1$ being the principal eigenvalue of the p-Laplacian with the Dirichlet boundary conditions.
5
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A random nonlinear multivalued evolution equation in Hilbert space

100%
Kravvaritis D., Papageorgiou N. S.
Colloquium Mathematicum
|
1989-1990
|
tom 58
|
nr 1
131-143
6
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Boundary value problems for evolution inclusions

99%
Papageorgiou N. S.
Annales Polonici Mathematici
|
1989-1990
|
tom 50
|
nr 3
251-259
7
Content available remote

On transition multimeasures with values in a Banach space

70%
Papageorgiou N. S.
Studia Mathematica
|
1990
|
tom 97
|
nr 1
37-51
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