Scurtă prezentare a proiectului

Prezentul proiect îşi propune studiul unor clase eliptice de incluziuni diferenţiale şiinegalităţi hemivariaţionale definite pe domenii nemărginite şi pe varietăţi Riemann  prin utilizarea unor metode variaţionale recente. Acest studiu este motivat de numeroase fenomene discontinue, ce apar în natură, în mecanica fluidelor, în mecanica cuantică, în teoria câmpului. Direcţii de cercetare:

1. Probleme eliptice cu discontinuităţi pe domenii nemărginite
2. Probleme nenetede de valori proprii cu şi fără restricţii

Soluţiile problemelor studiate sunt punctele critice ale funcţionalei de energie ataşată problemei, ele reprezentând stările de echilibru ale unor sisteme din mecanică. În mecanica cuantică şi în teoria câmpului aceste probleme descriu  stările particulelor elementare, când nivelul de energie se schimbă, influenţând comportarea ondulatorie a acestora. Pentru obţinerea rezultatelor teoretice se vor aplica metode variaţionale, precum principiul neneted al simetriei critice, metoda Fibering a lui Pohozaev şi principiul variaţional al lui Ricceri. Aceste rezultate vizează existenţa, multiplicitatea şi comportamentul asimptotic al soluţiilor.

Membrii echipei de cercetare

Articole publicate

1. Alexandru Kristály, Ioana Lazăr, Nikolaos S. Papageorgiou, A variational inequality on the half line, Nonlinear Analysis. Theory, Methods & Applications, Volume 71, Issue 10, (2009), 5003-5009 (ISI)


2. Michael Filippakis, Alexandru Kristály, Nikolaos S. Papageorgiou, Existence of five nonzero solutions with exact sign for a $p$-Laplacian equation. Discrete Contin. Dyn. Syst. 24 (2009), no. 2, 405-440 (ISI)


3. Hannelore Lisei, Csaba Varga, Multiple Solutions for a Differential Inclusion Problem with Nonhomogeneous Boundary Conditions. Numerical Functional Analysis and Optimization, 30 (2009) 566-581 (ISI)


4. Alexandru Kristály, Csaba Varga, Variational-Hemivariational Inequalities on Unbounded Domains. Studia Univ. Babes-Bolyai, Mathematica, LV, Nr. 2 (2010) 3-87


5. Hannelore Lisei, Ioana Lazăr, Application of a Three Critical Point Theorem for a Class of Inclusion Problems. Mathematica (Romanian Academy), Vol. 53 (76), No. 2 (2011)


6. Alexandru Kristály, Waclaw Marzantowicz, Csaba Varga, A non-smooth three critical points theorem with applications in differential inclusions. J. Glob. Optim. 46 (2010), 49–62, DOI 10.1007/s10898-009-9408-0 (ISI)


7. Alexandru Kristály, On singular elliptic equations involving oscillatory terms. Nonlinear Analysis 72 (2010) 1561-1569 (ISI)


8. Hannelore Lisei, Csaba Varga, Multiple Solutions for Gradient Elliptic Systems with Nonsmooth Boundary Conditions. Mediterranean Journal of Mathematics 8 (2010), 69-79, DOI 10.1007/s00009-010-0052-1. (ISI)


9. Wilfried Grecksch, Hannelore Lisei, Stochastic Nonlinear Equations of Schrödinger Type. Va apărea în : Stochastic Analysis and Applications (ISI)


10. Monica Bota, Andrea E. Molnár, Csaba Varga, On Ekeland’s variational principle in b-metric spaces. Va apărea în : International Journal on Fixed Point Theory, Computation and Applications (ISI)


11. Andrea E. Molnár, A Nonsmooth Sublinear Elliptic Problem in R^N with Perturbations. Va apărea în : Studia Univ. Babes-Bolyai, Ser. Mathematica


12. Wilfried Grecksch, Hannelore Lisei, Stochastic Schrödinger Equation Driven by Cylindrical Wiener Process and Fractional Brownian Motion. Va apărea în : Studia Univ. Babes-Bolyai, Ser. Mathematica Volume LVI, Number 2, 381-391 (2011)


13. Hannelore Lisei, Andrea E. Molnár, Csaba Varga, On a class of inequality problems with lack of compactness. Journal of Mathematical Analysis and Applications 378, 741-748 (2011), DOI 10.1016/j.jmaa.2010.12.041 (ISI)


14. Francesca Faraci,Antonio Iannizzoto, Alexandru Kristaly, Low dimensional compact embeddings of symmetric Sobolev spaces and applications. Proceedings of the Royal Society of Edinburgh 141 A, 383–395 (2011) (ISI)


15. Dusan Repovs, Csaba Varga, Nash Type Solution for Hemivariational Inequality Systems. Nonlinear Analysis TMA 74, 5585–5590 (2011) (ISI)


16. Alexandru Kristály, Ildiko Mezei, Multiple Solutions for a Perturbed System on Strip-Like Domains. Va apărea în : Discrete and Continuous Dynamical Systems Series S, Vol. 5, No. 4, August 2012

Comunicări la conferinţe şi seminarii de cercetare

Cs. Varga

1. Universita degli Studi di Perugia (Perugia, Italia), Dipartimento di Matematica e Informatica: A non-smooth three critical points theorem with applications in differential inclusions. (23.09.2009)


2. la Universita degli Studi di Perugia (Perugia, Italia), Dipartimento di Matematica e Informatica: Infinitely many solutions for a class of inhomogeneous Neumann problems. (30.09.2009)

A. Kristály

1. Faculty of Mathematics and Informatics, Ovidius University Constanta, Romania: Weber-type problems and Nash equilibria: a geometrical approach. (21.05.2010)


2. IMAR Montly Lectures, Bucharest, Romania: Elliptic problems involving oscillatory nonlinearities. (17.11.2010)


3. 7th Bolyai-Gauss-Lobachevsky Conference, Cluj-Napoca, Romania: Nash-Stampacchia equilibrium points on Riemannian manifolds. (05.-09.07.2010)

H. Lisei

1. Seminarul de Cercetare al Catedrei de Calcul Numeric şi Statistic de la Facultatea de Matematică şi Informatică a Universităţii Babeş-Bolyai din Cluj-Napoca: Soluţii multiple pentru ecuaţii neliniare generate de forme Dirichlet pe domenii fractale. (10.03.2009)


2. GAMM-Workshop "Stochastische Modelle und Steuerung" Lutherstadt Wittenberg, Germania: Multiple Solutions for Nonlinear Equations Involving Dirichlet Forms. (16 - 19.03.2009)


3. Romanian-German Symposium on Mathematics and Its Applications -Workshop in Nonlinear Analysis and Mathematical Physics, Sibiu: Multiple Solutions for Nonlinear Equations Involving Dirichlet Forms. (14-17.05.2009)


4. Faculty of Mathematics and Computer Science Babes-Bolyai University, Cluj-Napoca, Romania: Stochastic Nonlinear Equations of Schrödinger Type. (28.04.2010)


5. 8th AIMS Conference on Dynamical Systems, Differential Equations and Applications, Technical University Dresden, Germany: Solutions for Stochastic Equations of Schrödinger Type. (25.–28.05.2010)


6. Deterministic and stochastic variational methods and applications - Workshop, Martin-Luther Universität Halle-Wittenberg, Germany: Stochastic Schrödinger Equations. (07.-20.11.2010)


7. Invited Talk: Institute for Mathematics Paderborn University, Germany: Stochastic Schrödinger Equations.. (19.07.2010)

A. Molnar

1. Transilvanian Student Conference on Science, Cluj-Napoca, Romania: Variational principles and applications. (14-16.05.2010)


2. Deterministic and stochastic variational methods and applications - Workshop, Martin-Luther Universität Halle-Wittenberg, Germany: Ekeland’s variational principle in b-metric spaces. (07.-20.11.2010)