Nikolaos S Papageorgiou
Articles written in Proceedings – Mathematical Sciences
Volume 102 Issue 1 April 1992 pp 59-71
In this paper we study maximal monotone differential inclusions with memory. First we establish two existence theorems; one involving convex-valued orientor fields and the other nonconvex valued ones. Then we examine the dependence of the solution set on the data that determine it. Finally we prove a relaxation theorem.
Volume 103 Issue 2 August 1993 pp 181-195
In this paper we present new versions of the set-valued Fatou’s lemma for sequences of measurable multifunctions and their conditional expectations. Then we use them to study the continuity and measurability properties of parametrized set-valued integrals.
Volume 108 Issue 2 June 1998 pp 179-187
In this paper we examine nonlinear parabolic problems with a discontinuous right hand side. Assuming the existence of an upper solution φ and a lower solution ψ such that ψ ≤ φ, we establish the existence of a maximum and a minimum solution in the order interval [ψ, φ]. Our approach does not consider the multivalued interpretation of the problem, but a weak one side “Lipschitz” condition on the discontinuous term. By employing a fixed point theorem for nondecreasing maps, we prove the existence of extremal solutions in [ψ, φ for the original single valued version of the problem.
Volume 109 Issue 2 May 1999 pp 211-230
In this paper we consider two quasilinear boundary value problems. The first is vector valued and has periodic boundary conditions. The second is scalar valued with nonlinear boundary conditions determined by multivalued maximal monotone maps. Using the theory of maximal monotone operators for reflexive Banach spaces and the Leray-Schauder principle we establish the existence of solutions for both problems.
Volume 111 Issue 1 February 2001 pp 107-125
In this paper we study second order scalar differential equations with Sturm-Liouville and periodic boundary conditions. The vector field
Volume 111 Issue 4 November 2001 pp 489-508
In this paper we study nonlinear elliptic boundary value problems with monotone and nonmonotone multivalued nonlinearities. First we consider the case of monotone nonlinearities. In the first result we assume that the multivalued nonlinearity is defined on all ℝ. Assuming the existence of an upper and of a lower solution, we prove the existence of a solution between them. Also for a special version of the problem, we prove the existence of extremal solutions in the order interval formed by the upper and lower solutions. Then we drop the requirement that the monotone nonlinearity is defined on all of ℝ. This case is important because it covers variational inequalities. Using the theory of operators of monotone type we show that the problem has a solution. Finally in the last part we consider an eigenvalue problem with a nonmonotone multivalued nonlinearity. Using the critical point theory for nonsmooth locally Lipschitz functionals we prove the existence of at least two nontrivial solutions (multiplicity theorem).
Volume 113 Issue 3 August 2003 pp 293-319
In this paper we study nonlinear second-order differential inclusions involving the ordinary vector
Volume 114 Issue 3 August 2004 pp 269-298
In this paper we study second order non-linear periodic systems driven by the ordinary vector
Volume 116 Issue 2 May 2006 pp 233-255 Regular Articles
We consider a semilinear elliptic equation with a nonsmooth, locally Lipschitz potential function (hemivariational inequality). Our hypotheses permit double resonance at infinity and at zero (double-double resonance situation). Our approach is based on the nonsmooth critical point theory for locally Lipschitz functionals and uses an abstract multiplicity result under local linking and an extension of the Castro-Lazer-Thews reduction method to a nonsmooth setting, which we develop here using tools from nonsmooth analysis.