On a non-homogeneous eigenvalue problem involving a potential: an Orlicz-Sobolev space setting

By Mihai Mihuailescu, V. Ruadulescu, Dušan D. Repovš. 2016

58 citations recorded by the source corpus.

In this paper we study a non-homogeneous eigenvalue problem involving variable growth conditions and a potential V . The problem is analyzed in the context of Orlicz–Sobolev spaces. Connected with this problem we also study the optimization problem for the particular eigenvalue given by the infimum of the Rayleigh quotient associated to the problem with respect to the potential V when V lies in a bounded, closed and convex subset of a certain variable exponent Lebesgue space. © 2009 Elsevier Masson SAS. All rights reserved. Résumé Dans cet article on étudie un problème non homogène à valeurs propres avec exposant variable et potentiel V . Ce problème est analysé dans les espaces d’Orlicz–Sobolev. On étudie également le problème d’optimisation dans le cas particulier où la valeur propre s’obtient par minimisation du quotient de Rayleigh associé au potentiel V , quand V appartient à un ensemble borné, fermé et convexe d’un espace de Lebesgue à exposant variable. © 2009 Elsevier Masson SAS. All rights reserved. MSC: 35D05; 35J60; 35J70; 58E05; 68T40; 76A02

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/ce46aa9a411e96125e767a0876f5cd01224afeda

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Citations in the corpus

Overview of differential equations with non-standard growth (2010, unknown): “Later, Mihăilescu, Rădulescu and Repovš [155] generalized (6.”
Strauss- and Lions-type results for a class of Orlicz-Sobolev spaces and applications (2013, methodology): “We cite the papers of Bonanno, Bisci and Radulescu [5, 6], Cerny [7], Clément, Garcia-Huidobro and Manásevich [8], Donaldson [11], Fuchs and Li [14], Fuchs and Osmolovski [15], Fukagai, Ito and Narukawa [16, 17], Gossez [18], Le and Schmitt [19], Mihailescu and Radulescu [21, 22], Mihailescu and Rep”
Existence of Positive Solutions for p(x)-Laplacian Equations with a Singular Nonlinear Term (2014, background): “For example, the regularity of weak solutions for differential equations with variable exponent was studied in [1, 7], and existence of solutions for variable exponent problems was studied in a series of papers [3, 9, 12, 20, 24, 30, 33, 36, 39, 44, 45].”