Project Title: Differential Inclusions and Nonsmooth Variational Problems in Nonlinear Analysis and Applications
Project Number: PN-II-RU-PD-2011-3-0032
Members: Nicușor COSTEA (Director), Vicențiu RĂDULESCU (Adviser)
Abstract: We are concerned with the study of some nonsmooth variational problems and their applications to nonsmooth mechanics. The goal is to investigate the existence, non-existence, multiplicity and qualitative properties of solutions for some inequality problems and nonlinear elliptic (parabolic) differential inclusions. We are insterested in finding mathematical results with applications in mathematical physics, in the sense that the inequalities and differential inclusions that will be analyzed can serve as models for various physical phenomena. Three directions of research will be considered:
Differential inclusions involving the presence of a quasilinear/nonhomogeneous operator and a multivalued function given by Clarke's generalized gradient;
Inequality problems and systems of inequalities of hemivariational type;
Problems describing the contact between a deformable body and a foundation.
Papers:
N. Costea, D.A. Ion & C. Lupu, Variational-like inequality problems involving set-valued maps and generalized monotonicity, Journal of Optimization Theory and Applications, 155 (1) (2012), 79-99. [pdf]
N. Costea & Cs. Varga, Systems of nonlinear hemivariational inequalities and applications, Topological Methods in Nonlinear Analysis 41 (1) (2013), 39-67. [pdf]
I. Andrei, N. Costea & A. Matei, Antiplane shear deformation of piezoelectric bodies in contact with a conductive support, Journal of Global Optimization 56 (1) (2013), 103-119. [pdf]
N. Costea & Cs. Varga, Multiple critical points for non-differentiable parametrized functionals and applications to differential inclusions, Journal of Global Optimization, 56 (2) 2013, 399-416. [pdf]
N. Costea & G. Morosanu, A multiplicity result for an elliptic anisotropic differential inclusion involving variable exponents, Set-Valued and Variational Analysis, 21 (2013), 311-322. [pdf]
N. Costea, I. Firoiu & F. Preda, Elliptic boundary value problems with nonsmooth potential and mixed boundary conditions, Complex Variables and Elliptic Equations 58 (9) (2013), 1201-1213. [pdf]
Talks:
Differential inclusions depending on a real parameter, Advances in Differential Equations: Symmetrizations and related topics, Faculty of Mathematics and Computer Science, Babes-Bolyai University (Cluj-Napoca, Romania), March 14-15, 2013.
https://sites.google.com/site/idei0241/mini-workshop
Differential inclusions depending on a real parameter, Workshop for Young Researchers in Mathematics, Faculty of Mathematics and Computer Science, Ovidius University (Constanta, Romania), May 9-10, 2013.
http://math.univ-ovidius.ro/Workshop/2013/WYRM/GeneralInfo.htm
Multiplicity of critical points for non-smooth parametrized functionals, Joint international meeting of the American Mathematical Society and the Romanian Mathematical Society in partnership with Simion Stoilow Institute of Mathematics of the Romanian Academy, "1 Decembrie 1918" University of Alba-Iulia (Alba-Iulia, Romania), June 27-30, 2013.
http://imar.ro/ams-ro2013/description.php
Documents