Abstracts - Facultatea de Matematică

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We obtain results concerning Newton interpolating series and their derivatives and sufficient conditions for a function to be representable into a Newton interpolating series. The representation of solutions of particular differential equations through Newton interpolating series are also considered. Pareto reducibility and contractibility in vector optimization Nicolae POPOVICI Babe¸s-Bolyai University of Cluj, Romania popovici@math.ubbcluj.ro A multicriteria optimization problem is said to be Pareto reducible if the set of weakly efficient solutions can be represented as the union of the sets of (Pareto) efficient solutions of its subproblems (i.e. optimization problems obtained from the original one by selecting certain criteria). The principal aim of this presentation is to provide sufficient conditions for Pareto reducibility, under appropriate generalized convexity assumptions. We will also show that Pareto reducibility is intimately related to the contractibility of efficient sets. References: [1] J. Benoist, Contractibility of efficient frontier of simply shaded sets, Journal of Global Optimization 25, (2003), 321–335. [2] N. Popovici, Pareto reducible multicriteria optimization problems, Optimization 54, (2005), 253–263. [3] N. Popovici, Structure of efficient sets in lexicographic quasiconvex multicriteria optimization, Operations Research Letters 34, (2006), 142–148. Singular phenomena in nonlinear elliptic problems Vicent¸iu RĂDULESCU Department of Mathematics, University of Craiova 200585 Craiova, Romania vicentiu.radulescu@math.cnrs.fr We consider two classes of nonlinear elliptic equations and we are concerned with the existence and the uniqueness of solutions, as well as with the study of the growth of solutions near the boundary. We first consider singular solutions of the logistic equation in anisotropic media and we discuss the blow-up rate of solutions in terms of Karamata’s regular variation theory. Next, we establish several bifurcation results for the Lane- Emden-Fowler equation with singular nonlinearity and convection term. 36
Functional monotone VP and normed coercivity Mihai Turinici “A. Myller” Mathematical Seminar; “Al. I. Cuza” University 11, Copou Boulevard; 700506 Ia¸si, Romania mturi@uaic.ro A functional extension is given for the monotone variational principle in Turinici [An. St. UAIC Iasi, 36 (1990), 329–352]. The obtained facts are then applied to establish (via conical Palais–Smale techniques) a monotone functional version of the coercivity result in Zhong [Nonlinear Analysis, 29 (1997), 1421–1431]. Viability for Nonlinear Reaction-Diffusion Systems Mihai NECULA and Ioan I. VRABIE Faculty of Mathematics, “Al. I. Cuza” University of Ia¸si, Romania necula@uaic.ro Faculty of Mathematics, “Al. I. Cuza” University of Ia¸si “O. Mayer” Mathematics Institute of the Romanian Academy, Ia¸si, Romania ivrabie@uaic.ro We prove several necessary and/or sufficient conditions for viability for certain classes of nonlinear reaction-diffusion systems governed by continuous perturbations of mdissipative operators. Integro-differential hamilton-jacobi-bellman equations associated to SDES driven by stable processes A. ZĂLINESCU Laboratoire de Mathématiques et Applications Université de La Rochelle, Avenue Michel Crépeau 17042 La Rochelle, France azalines@univ-lr.fr We are interested in the way in which (nonlinear) Hamilton–Jacobi–Bellman equations (or variational inequalities) involving an integro-differential operator relate to jump diffusion processes via optimal stochastic control (and optimal stopping) problems. Our main domain of interest lies in the case where the dynamics has infinite variance, especially in the case where the jump diffusion process is a solution of a SDE driven by stable processes. We prove that the value function of the optimal control problem is a viscosity solution of the integro-differential variational inequality arising from the associated dynamic 37
Page 1: Faculty of Mathematics University
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Page 42 and 43: A Stability Theorem for Functional
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Page 50 and 51: Joint work with Stephen Joe (Univer
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Abstracts - Facultatea de Matematică

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