FCT-FEDER Project POCI/MAT/55524/2004:
DIFFERENTIAL INCLUSIONS AND VARIATIONAL PROBLEMS
FCT-FEDER Project POCI/MAT/55524/2004:
DIFFERENTIAL INCLUSIONS AND VARIATIONAL PROBLEMS
Research team / Equipa de investigação
|
Vasile Staicu |
Principal Investigator |
|
Luís Filipe Pinheiro Castro |
Investigator |
|
Vladimir Vladimirovich Goncharov |
Investigator |
|
|
|
|
Eugénio Alexandre Miguel Rocha |
Investigator |
|
Mihai Vornicescu |
Investigator |
|
Sandrina Rafaela Andrade Santos |
Bolseira / Doutoramento |
Abstract
Our aim is to investigate various problems of differential inclusions and minimum problems for nonconvex integral functionals of the gradient, mainly without convexity assumptions. We presume to obtain new results concerning:
(a) existence, uniqueness, asymptotic properties and continuous dependence on data, of solutions to classes of nonlinear multivalued evolution equations in Banach spaces. We will consider both differential and functional-differential equations governed by set-valued operators. Of concern are initial and boundary value problems of theoretical and practical significance. For functional equations characterized by integral equations having a kernel depending on lag functions we will look for existence and uniqueness results of the solutions, in different classes of spaces. We expect results concerning existence, uniqueness and differentiability with respect to the lag, as well as concerning initial-value problems for partial differential equations with time delay solved by integral equations methods.
(b) Total differential inclusions: develop the method of superior and inferior solutions; study the existence of solutions to total differential inclusions depending continuously by the afin data on the boundary; compaire the method of inferior and superior solutions with the Baire category methods and the Gromov´s convex integration method; construct extremal solutions to nonconvex total inclusions and prove their density into the set of solutions of the convexified problem.
(c) minimum problems for nonconvex integral functional depending on the gradient. We are interested to study: the validity of the Euler-Lagrange equation in the sense of convex analysis, regularity and Lavrentiev fenomenon; existence of continuous solutions with respect to the affine data on the boundary; how to apply the method of superior and inferior solutions to problems with nonlinear boundary data, to problems where the integrand also depends of the function not only of its gradient and to vectorial problems. Finally we want to study some applications to nonlinear elasticity.
Project Objectives (description)
The main objectives of the project are:
(a) to benefit the professional development of the members of the team by enabling them to make progress in their investigation of some important open research questions, which will hopefully result in new publications.
(b) to develop and consolidate a research group at the Aveiro University interested in the theory of multivalued differential equations, calculus of variations and their interactions, by direct young researchers to the study of such fields and supervise young students.
(c) to facility and promote the interaction between two research groups interested in the theory of differential inclusions, calculus of variations and their interactions, from Aveiro and Evora. To this aim a monthly joint seminar and mincourses are planed.
(d) to collaborate with colleags from abroad (Italy, USA and Japan) to research and co-supervising, that will also have a positive impact on our graduate programs, since we will be able to share new results, research directions and methods with our Ph.D. students, and offer them new dissertation topics.
Tasks
Indicadores de realização física
| A - Publicações |
2005-2008 |
| Livros | 2 |
| Artigos em revistas internacionais | 40 |
| Artigos em Proceedings de Conf. Internacionais | 2 |
| B- Comunicações | |
| Em congressos científicos internacionais | 9 |
| Em seminários de investigação | |
| C- Relatórios | 5 |
| D- Organização de seminários e conferências | 4 |
| E- Formação Avançada | |
| Teses de Doutoramento concluídas | 1 |
| Teses de Doutoramento em progresso | 1 |
| Teses de Mestrado concluídas | 1 |
| Teses de Mestrado (em progresso | 1 |
Publicações
Books:
B1. Differential Equations, Chaos and Variational Problems (V. Staicu, Ed.), Birkhauser, Bassel, 2007, 435 p., Hardcover, ISBN: 978-3-7643-8481-4.
B2. S. Aizicovici, N. S. Papageorgiou, V. Staicu: Degree theory for operators of monotone type and nonlinear elliptic equations with inequality constr aints, Memoirs of the American Mathematical Society 2008; 70 pp; softcover, Volume: 196, ISBN-10: 0-8218-4192-0, ISBN-13: 978-0-8218-4192-1
Papers in international journals with referee
PRJ1. S. Aizicovici, V. Staicu: Continuous selections of solution sets to Volterra integral inclusions in Banach spaces, Electronic Journal of Diffe rential Equations, 2006(2006), No. 1, pp. 1-11.
PRJ2. S. Aizicovici, N. S. Papageorgiou, V. Staicu: Periodic solutions for second order differential inclusions with scalar p-Laplacian, Journal of Ma thematical Analysis and Applications, 322, 2006, 913-929.
PRJ3. S. Aizicovici, N. S. Papageorgiou, V. Staicu: Resonant nonlinear periodic problems with the scalar p-Laplacian and a nonsmmoth potential, Topolo gical Methods in Nonlinear Analysis, 27, 2006, 269-288.
PRJ4. S. Aizicovici, N. S. Papageorgiou, V. Staicu: Periodic solutions of nonlinear evolution inclusions in Banach space, Journal of Nonlinear and Con vex Analysis, 7, 2006, 163-177.
PRJ5. L. P. Castro, A. H. Kamel: Mathieu function and Kontorovich-Lebedev transforms in the L-shaped wave scattering problem, African Diaspora Journal of Mathematics, 5, 2006, 55-71.
PRJ6. L. P. Castro, D. Natroshvili: The reactance wave diffraction problem by a strip in a scale of Bessel potential spaces, Opuscula Mathematica, 26, 2006, 289-303.
PRJ7. L. P. Castro, D. Natroshvili: The potential method for the reactance wave diffraction problem in a scale of spaces, Georgian Mathematical Journa l, 13, 2006, 251-260.
PRJ8. E. A. M. Rocha and D. F. M. Torres, Quadratures of Pontryagin Extremals for Optimal Control Problems, Control & Cybernetics, 35(2006), 947-963
PRJ9. P. D. F. Gouveia, D. F. M. Torres and Eugénio A. M. Rocha, Symbolic Computation of Variational Symmetries in Optimal Control, Control & Cybernet ics, 35(2006) 832-849.
PRJ10. N. S. Papageorgiou and V. Staicu: The method of upper-lower solutions to nonlinear second order differential inclusions, Nonlinear Anal. 67(200 7), 708-726.
PRJ11. N. S. Papageorgiou and V. Staicu: Multiple solutions for strongly resonant periodic systems, Nonlinear Analysis, 67(2007), 1895-1907.
PRJ12. S. Aizicovici, N. S. Papageorgiou and V. Staicu: Multiple nontrivial solutions for nonlinear periodic problems with the p-Laplacian, J. Differential Equations, 243(2007), 504-535.
PRJ13. S. Aizicovici and V. Staicu: Multivalued evolution equations with nonlocal initial conditions in Banach spaces, Nonlinear Differential Equation s and Applications, 14(2007), 361-376.
PRJ14. L. P. Castro, D. Kapanadze: On wave diffraction by a half-plane with different face impedances, Mathematical Methods in the Applied Sciences, 3 0, 2007, 513-527.
PRJ15. L. P. Castro, D. Kapanadze: A Boundary-Transmission Problem with first and second kind conditions for the Helmholtz equation in Besov and Besse l potential spaces, Bull. Greek Math. Soc., 54, 2007, 79-96.
PRJ16. N. S. Papageorgiou, E. Rocha and V. Staicu: A multiplicity theorem for hemivariational inequalities with p-Laplacian like differential operator , Nonlinear Anal., 69(2008), 1150-1163.
PRJ17. N. S. Papageorgiou, S. R. Andrade Santos and V. Staicu: Three nontrivial solutions for the p-Laplacian with a nonsmooth potential, Nonlinear A nal. 68(2008), 3812-3827.
PRJ18. M. E. Filippakis, N. S. Papageorgiou and V. Staicu: Eigenvalue problems for nonlinear elliptic equations with unilateral constraints, Nonlinear Anal., 69(2008), 85-109.
PRJ19. N. S. Papageorgiou, E. Rocha and V. Staicu: Multiplicity theorems for superlinear elliptic problems, Calc. Var. Partial Differential Equations, 33(2008), 199-230.
PRJ20. N. S. Papageorgiou, E. Rocha: A multiplicity theorem for a variable exponent Dirichlet problem, Glasgow Math. Journal 50(2008), 1–15.
PRJ21. M. E. Filippakis, N. S. Papageorgiou and V. Staicu: Positive Solutions for Nonlinear Periodic Problems, Positivity, 12 (2008), 733–750.
PRJ22. E. Rocha and D. Torres: First integrals for problems of the calculus of variations on locally convex spaces, E. J. Appl. Sci. 10(2008), 207–218 .
PRJ23. L. P. Castro and D. Kapanadze: “Pseudo-differential Operators in a Wave Diffraction Problem with Impedance Conditions”, Fractional Calculus & A pplied Analysis 11 (2008), 15–26.
PRJ24. L. P. Castro and D. Kapanadze: “Dirichlet-Neumann-Impedance Boundary-Value Problems Arising in Rectangular Wedge Diffraction Problems”, Proceed ings of the American Mathematical Society 136 (2008), 2113–2123.
PRJ25. L. P. Castro and D. Kapanadze: “Wave Diffraction by a Strip with First and Second Kind Boundary Conditions: the Real Wave Number Case”, Mathem atische Nachrichten 281(10) (2008), 1400–1411.
PRJ26. N. S. Papageorgiou, E. Rocha: A multiplicity theorem for a variable exponent Dirichlet problem, Glasgow Math. Journal 50(2008), 1–15.
PRJ27. N. S. Papageorgiou, S. R. Andrade Santos and V. Staicu: Eigenvalue problems for hemivariational inequalities, Set-Valued Analysis, 16(2008), 1 061-1087.
PRJ28. A. Cellina and M. Vornicescu: On the existence of solutions to a special variational problem, Calculus of Variations (accepted for publication) .
PRJ29. N. S. Papageorgiou and V. Staicu: Multiple nontrivial solutions for doubly resonant periodic problems, Canadian Math. Bull. (accepted for publication).
PRJ30. S. Aizicovici, N. S. Papageorgiou and V. Staicu: The spectrum and an index formula for the Neumann p-Laplacian and multiple solutions for prob lems with crossing nonlinearity, Discrete and Continuous Dynamical Systems, (accepted for publication).
PRJ31. N. S. Papageorgiou, S. R. Andrade Santos and V. Staicu: On the existence of nontrivial solutions for resonant Neumann problems, Journal of Non linear and Convex Analysis, (accepted for publication).
PRJ32. S. Aizicovici, N. S. Papageorgiou and V. Staicu: Existence of multiple solutions with precise sign information for superlinear Neumann problem s, Ann. Mat. Pura Appl. (accepted for publication).
PRJ33. S. Aizicovici, N. S. Papageorgiou and V. Staicu: Multiple positive solutions for a p-Laplacian Dirichlet problem with superdiffusive reaction, Houston J. Math. (accepted for publication).
PRJ34. S. Aizicovici, N. S. Papageorgiou and V. Staicu: On a p-superlinear Neumann p-Laplacian equation, Topological Meth. Nonlinear Anal. (accepted f or publication).
PRJ35. E.M. Rocha and M.M. Rodrigues, The speed of reaction-diffusion- convection wave-fronts in nonuniform media, Proceedings of the American Institute of Physics Journal, (accepted for publication).
PRJ36. N. S. Papageorgiou, E. Rocha: Pairs of positive solutions for p-Laplacian equations with sublinear and superlinear nonlinearities which do n ot satisfy the AR-conditions, Nonlinear Analysis, pp.16, (accepted for publication).
PRJ37. N. S. Papageorgiou, E. Rocha and V. Staicu: On the existence of three nontrivial smooth solutions for nonlinear elliptic equations, Math. Nachr. (submitted).
PRJ38. N. S. Papageorgiou, S. R. Andrade Santos and V. Staicu: Nontrivial solutions for nonvariational quasilinear Neumann problems, Topological M eth. Nonlinear Anal. (submitted).
PRJ39. N. S. Papageorgiou, E. Rocha and V. Staicu: On the existence of three nontrivial smooth solutions for nonlinear elliptic equations , Math. Nachr. (submitted).
PRJ40. N. S. Papageorgiou, S. R. Andrade Santos and V. Staicu: Nontrivial solutions for nonvariational quasilinear Neumann problems, Topological M eth. Nonlinear Anal. (submitted).
Papers in proceedings of international journals with referee
PICP1. V. Staicu: New results concerning evolution inclusions in Banach spaces, Conference on Differential & Difference Equations and Applications, Au gust 1-5, 2005, Melbourne, Fl., Ravi P. Agarwal, and Kanishka Perera, 1019-1027, Hindawi Publishing Corporation, 2006.
PCP3. S. Aizicovici, N. S. Papageorgiou and V. Staicu: Three nontrivial solutions for the p-Laplacian Neumann problems with a concave nonlinearity nea r the origin, Proceedings of the Conference on Nonlinear Analysis and Optimization in celebration of Alex Ioffe’s 70th and Simeon Reich’s 60th birthdays, June 18-24, 2008, Technion, Haifa, Israel, Israel Math. (Editors: Arie Leizarowitz, Boris Mordukhovich, Itai Shafrir, Alexander Zaslavski) (accept ed for publication
