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On Neumann boundary value problems for elliptic equations

Dimitrios A. Kandilakis — 2004

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

We provide two existence results for the nonlinear Neumann problem ⎧-div(a(x)∇u(x)) = f(x,u) in Ω ⎨ ⎩∂u/∂n = 0 on ∂Ω, where Ω is a smooth bounded domain in N , a is a weight function and f a nonlinear perturbation. Our approach is variational in character.

Evolution inclusions of the subdifferential type depending on a parameter

Dimitrios A. KandilakisNikolaos S. Papageorgiou — 1992

Commentationes Mathematicae Universitatis Carolinae

In this paper we study evolution inclusions generated by time dependent convex subdifferentials, with the orientor field F depending on a parameter. Under reasonable hypotheses on the data, we show that the solution set S ( λ ) is both Vietoris and Hausdorff metric continuous in λ Λ . Using these results, we study the variational stability of a class of nonlinear parabolic optimal control problems.

Periodic solutions for nonlinear evolution inclusions

Dimitrios A. KandilakisNikolaos S. Papageorgiou — 1996

Archivum Mathematicum

In this paper we prove the existence of periodic solutions for a class of nonlinear evolution inclusions defined in an evolution triple of spaces ( X , H , X * ) and driven by a demicontinuous pseudomonotone coercive operator and an upper semicontinuous multivalued perturbation defined on T × X with values in H . Our proof is based on a known result about the surjectivity of the sum of two operators of monotone type and on the fact that the property of pseudomonotonicity is lifted to the Nemitsky operator, which we...

Periodic solutions for nonlinear Volterra integrodifferential equations in Banach spaces

Dimitrios A. KandilakisNikolaos S. Papageorgiou — 1997

Commentationes Mathematicae Universitatis Carolinae

In this paper we examine periodic integrodifferential equations in Banach spaces. When the cone is regular, we prove two existence theorems for the extremal solutions in the order interval determined by an upper and a lower solution. Both theorems use only the order structure of the problem and no compactness condition is assumed. In the last section we ask the cone to be only normal but we impose a compactness condition using the ball measure of noncompactness. We obtain the extremal solutions...

Multiplicity of positive solutions for some quasilinear Dirichlet problems on bounded domains in n

Dimitrios A. KandilakisAthanasios N. Lyberopoulos — 2003

Commentationes Mathematicae Universitatis Carolinae

We show that, under appropriate structure conditions, the quasilinear Dirichlet problem - div ( | u | p - 2 u ) = f ( x , u ) , x Ω , u = 0 , x Ω , where Ω is a bounded domain in n , 1 < p < + , admits two positive solutions u 0 , u 1 in W 0 1 , p ( Ω ) such that 0 < u 0 u 1 in Ω , while u 0 is a local minimizer of the associated Euler-Lagrange functional.

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