@article{ 11589_7958, author = { Devillanova G and Solimini S and Tintarev C }, title = {On weak convergence in metric spaces}, year = {9999}, journal = {COMMUNICATIONS IN CONTEMPORARY MATHEMATICS}, abstract = {Abstract. This note gives an exposition of various extensions of the notion of weak convergence to metric spaces. They are motivated by applications, such as existence of xed points of non-expansive maps, and analysis of the defect of compactness relative to gauge groups in Banach spaces, where weak convergence is generally less useful than respectively, asymptotic centers in [14] and polar convergence in a preliminary version of [35]). The note compares notions of convergence of weak type found in literature, in particular the notion of -convergence introduced by Lim in [25], polar convergence introduced by the authors, and the modes of convergence of weak type introduced by Jost [20], Sosov [36] and Monod [28] in Hadamard spaces. Some applications of polar convergence, such as the existence of xed points for nonexpansive maps and a suitable variant of the Brezis-Lieb Lemma are produced.}, keywords = {polar convergence; delta convergence; fixed points; Brezis-Lieb Lemma} } @article{ 11589_3186, author = { Devillanova G and Solimini S and Tintarev C }, title = {On weak convergence in metric spaces}, year = {9999}, journal = {COMMUNICATIONS IN CONTEMPORARY MATHEMATICS}, abstract = {Abstract. This note gives an exposition of various extensions of the notion of weak convergence to metric spaces. They are motivated by applications, such as existence of xed points of non-expansive maps, and analysis of the defect of compactness relative to gauge groups in Banach spaces, where weak convergence is generally less useful than respectively, asymptotic centers in [14] and polar convergence in a preliminary version of [35]). The note compares notions of convergence of weak type found in literature, in particular the notion of -convergence introduced by Lim in [25], polar convergence introduced by the authors, and the modes of convergence of weak type introduced by Jost [20], Sosov [36] and Monod [28] in Hadamard spaces. Some applications of polar convergence, such as the existence of xed points for nonexpansive maps and a suitable variant of the Brezis-Lieb Lemma are produced.}, keywords = {polar convergence; delta convergence; fixed points; Brezis-Lieb Lemma} } @conference{ 11589_20518, author = { Caponio E and Devillanova G and Maddalena F and Masiello A and Solimini S }, title = {Problems in Calculus of Variations and Nonlinear Analysis}, year = {2014}, publisher = {Cangemi Editore}, booktitle = {Proceedings of the ``1st Workshop on the State of the Art and Challenges of Research Efforts at POLIBA, 03--05 dicembre 2014, Bari, Italy}, pages = {227--331} } @article{ 11589_2764, author = { Devillanova G and Solimini S }, title = {Infinitely Many Positive Solutions to Some Nonsymmetric Scalar Field Equations: the Planar Case}, year = {2014}, journal = {CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS}, volume = {52}, abstract = {We show the existence of infinitely many positive solutions u ∈ H1(R2) to the equation −Delta u + a(x)u = u^p, with p > 1 , without asking, on the positive potential a(x), any symmetry assumption as inWei and Yan (Calc Var Partial Differ Equ 37, 423–439, 2010) or Devillanova and Solimini (Adv Nonlinear Studies 12, 173–186, 2012) or small oscillation assumption as in Cerami et al. (Commun Pure Appl Math, doi:10.1002/cpa.21410, 2012) 6 and in Weiwei and Wei (Infinitely many positive solutions for Nonlinear equations with non-symmetric Potential, 2012).}, keywords = {Stationary Schr\"odinger equation in the whole domain; minimax theorem; concentration-compactness methods; profile decomposition}, url = {http://link.springer.com/article/10.1007%2Fs00526-014-0736-7}, doi = {10.1007/s00526-014-0736-7}, pages = {857--898} } @article{ 11589_52325, author = { Florio G and Devillanova G and Maddalena F }, title = {Blow-up of the quantum potential for a free particle in one dimension}, year = {2013}, journal = {IL NUOVO CIMENTO C}, volume = {36}, abstract = {We derive a non-linear differential equation that must be satisfied by the quantum potential, in the context of the Madelung equations, in one dimension for a particular class of wave functions. In this case, we exhibit explicit conditions leading to the blow-up of the quantum potential of a free particle at the boundary of the compact support of the probability density.}, keywords = {Quantum mechanics, Formalism, Ordinary differential equations}, pages = {83--93} } @article{ 11589_52188, author = { Devillanova G and Solimini S }, title = {Min-Max Solutions to Some Scalar Field Equations}, year = {2012}, journal = {ADVANCED NONLINEAR STUDIES}, volume = {12}, abstract = {Abstract We show the variational structure of a multiplicity result of positive solutions u is an element of H(1) (R(N)) to the equation -Delta u + a(x)u = u(p), where N >= 2, p > 1 with p < 2* - 1 = N+2/N-2 if N >= 3 and the potential a(x) is a positive function enjoying a planar symmetry. We require suitable decay assumptions which are widely implied by those in [6], in which Wei and Yan have obtained an analogous multiplicity result by using different techniques.}, keywords = {Stationary Schr¨odinger equation in the whole domain; minimax theorem; concentration-compactness methods}, url = {http://www.advancednonlinearstudies.com/Archive/V12N1/ANLS_V12N1_pg173-186.php}, pages = {173--186} } @inbook{ 11589_12427, author = { Devillanova G and Ligouras P }, title = {Human Resource Management e Matematica con LIM}, year = {2010}, publisher = {Scriptaweb}, address = {NAPOLI}, booktitle = {Formazione, Innovazione e Tecnologie}, url = {http://www.scribd.com/doc/159799811/Devillanova-Human}, pages = {273--287} } @article{ 11589_8788, author = { Devillanova G and Solimini S }, title = {On the dimension of a irrigable measure}, year = {2007}, journal = {RENDICONTI DEL SEMINARIO MATEMATICO DELL'UNIVERSITA' DI PADOVA}, volume = {117}, pages = {1--49} } @book{ 11589_24098, author = { Devillanova G}, title = {Singular Structures in some Variational Problem Structures singulières de quelques problèmes variationnels}, year = {2007}, publisher = {Atelier National de Reproducion de These}, address = {Grenoble}, abstract = {This thesis represents the synthesis of the results obtained during these last four years of research and study under the guide and teachings of professor S. Solimini and professor J.-M. Morel. In this thesis we approach some problems of Nonlinear Analysis and of Calculus of Variations which give rise to ``singular'' structures. Our purpose is to show how in some cases these singular structures are an obstacle to overcome to get existence or multiplicity results and in other cases the singularities in the solutions are the object of the study and justify the choice of the functional introduced. The work is divided into two parts: the first one concerns results on a class of problems, which have been faced by researchers in nonlinear analysis in the last twenty years, about the existence and the multiplicity of solutions of elliptic equations, obtained in spite of a lack of compactness due to some concentration phenomena; the second one regards a certain category of irrigation problems in which the trajectories followed by fluid particles give rise to a one-dimensional set and which can be set in the transport theory.}, keywords = {défaut de compacité; concentration; irrigation}, url = {http://hal.archives-ouvertes.fr/docs/00/13/26/80/PDF/Devillanova2005.pdf}, pages = {1--199} } @article{ 11589_2093, author = { Devillanova G and Solimini S }, title = {Elementary properties of optimal irrigation patterns}, year = {2007}, journal = {CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS}, volume = {28}, abstract = {In this paper we follow the approach in Maddalena et al. (Interfaces and1 Free Boundaries 5, 391–415, 2003) to the study of the ramified structures and we identify some geometrical properties enjoyed by optimal irrigation patterns. These properties are “elementary” in the sense that they are not concerned with the regularity at the ending points of such structures, where the presumable selfsimilarity properties should take place. This preliminary study already finds an application in G. Devillanova and S. Solimini (Math. J. Univ. Padua, to appear), where it is used in order to discuss the irrigability of a given measure.}, doi = {10.1007/s00526-006-0046-9}, pages = {317--349} }