Jump to ContentJump to Main Navigation
Show Summary Details
In This Section

Advances in Pure and Applied Mathematics

Editor-in-Chief: Trimeche, Khalifa

Managing Editor: Bezzarga, Mounir / Kamoun, Lotfi / Karoui, Abderrazek / Mili, Maher

Editorial Board Member: Sifi, Mohamed / Zaag, Hatem / Zarati, Said / Aldroubi, Akram / Anker, Jean-Philippe / Bahouri, Hajer / Baklouti, Ali / Bakry, Dominique / Beznea, Lucian / Bonami, Aline / Demailly, Jean-Pierre / Fleckinger, Jacqueline / Gallardo, Leonard / Ismail, Mourad / Jouini, Elyes / Maday, Yvon / Mustapha, Sami / Ovsienko, Valentin / Pouzet, Maurice / Radulescu, Vicentiu / Schwartz, Lionel / Kobayashi, Toshiyuki / Aouadi, Saloua / Baraket, Sami / Begehr, Heinrich / Ben Abdelghani, Leila / Jarboui, Noomen / Marzougui, Habib / Peigné, Mark

4 Issues per year

CiteScore 2016: 0.36

SCImago Journal Rank (SJR) 2015: 0.342
Source Normalized Impact per Paper (SNIP) 2015: 0.554

Mathematical Citation Quotient (MCQ) 2015: 0.33

See all formats and pricing
In This Section

Variational analysis for an indefinite quasilinear problem with variable exponent

Mabrouk Bouslimi
  • Institut Préparatoire aux Études d'Ingénieurs de Tunis, Université de Tunis, Rue Jawaher Lel Nehru, 1008 Montfleury, Tunis, Tunisia
  • Email:
/ Khaled Kefi
  • Institut Supérieur du Transport et de la Logistique de Sousse, Université de Sousse, 12 Rue Abdallah Ibn Zoubeir, 4029-Sousse, Tunisia
  • Email:
/ Felician-Dumitru Preda
  • Institute of Mathematical Statistics and Applied Mathematics, Calea 13 Septembrie 13, 050711 Bucharest, Romania
  • Email:
Published Online: 2012-01-19 | DOI: https://doi.org/10.1515/apam.2011.011


We study the nonlinear boundary value problem - div ((|u(x)|p1(x)-2+|u(x)|p2(x)-2u(x) =V1(x)|u|q(x)-2u-V2(x)|u|(x)-2u in , u=0 on , where is a bounded domain in N with smooth boundary, , are positive real numbers, p1, p2, q, are continuous functions on , V1 and V2 are weight functions in generalized Lebesgue spaces Ls1(x)() and Ls2(x)(), respectively, such that V1>0 in an open set 0 with |0|>0 and V20 on . We prove, under appropriate conditions that for any >0 there exists * sufficiently small such that for any (0,*) the above nonhomogeneous quasilinear problem has a nontrivial positive weak solution. The proof relies on some variational arguments based on Ekeland's variational principle.

Keywords.: p(x)$p(x)$-Laplace operator; generalized Sobolev spaces; mountain pass theorem; Ekeland's variational principle; weak solution

About the article

Received: 2011-04-20

Accepted: 2011-06-09

Published Online: 2012-01-19

Published in Print: 2012-01-01

Citation Information: Advances in Pure and Applied Mathematics, ISSN (Online) 1869-6090, ISSN (Print) 1867-1152, DOI: https://doi.org/10.1515/apam.2011.011. Export Citation

Comments (0)

Please log in or register to comment.
Log in