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An existence theorem for a strongly nonlinear elliptic problem in Musielak–Orlicz spaces

Volume 41 / 2014

Abdelmoujib Benkirane, Fatimazahra Blali, Mohamed Sidi El Vally Applicationes Mathematicae 41 (2014), 175-184 MSC: Primary 35J57; Secondary 35J60. DOI: 10.4064/am41-2-5

Abstract

We prove an existence result for some class of strongly nonlinear elliptic problems in the Musielak–Orlicz spaces $W^{1} L_{\varphi }(\varOmega )$, under the assumption that the conjugate function of $\varphi $ satisfies the $\Delta _2$-condition.

Authors

  • Abdelmoujib BenkiraneLaboratory LAMA Department of Mathematics
    Faculty of Sciences Dhar El Mahraz
    University Sidi Mohamed Ben Abdellah
    B.P. 1796 Atlas
    Fez, Morocco
    e-mail
  • Fatimazahra BlaliLaboratory LAMA Department of Mathematics
    Faculty of Sciences Dhar El Mahraz
    University Sidi Mohamed Ben Abdellah
    B.P. 1796 Atlas
    Fez, Morocco
    e-mail
  • Mohamed Sidi El VallyDepartment of Mathematics
    Faculty of Sciences
    King Khalid University
    Abha 61413, Kingdom of Saudi Arabia
    e-mail

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