Perturbed nonlinear degenerate problems in $\mathbb R^N $

Tom 36 / 2009

A. El Khalil, S. El Manouni, M. Ouanan Applicationes Mathematicae 36 (2009), 213-223 MSC: 35J60, 35J65, 35J70. DOI: 10.4064/am36-2-8

Streszczenie

Via critical point theory we establish the existence and regularity of solutions for the quasilinear elliptic problem $$ \left\{\eqalign{ &{-}\textrm{div} \mathcal{A}(x, \nabla u) + a(x)\vert u \vert^{p-2} u = g(x)|u|^{p-2}u + h(x)|u|^{s-1}u \quad\ \hbox{in } {\Bbb R}^N,\cr &u>0,\quad\ \lim_{\vert x \vert \rightarrow \infty} u(x) = 0,}\right. $$ where $ 1< p< N $; $ a(x) $ is assumed to satisfy a coercivity condition; $ h(x)$ and $ g(x)$ are not necessarily bounded but satisfy some integrability restrictions.

Autorzy

  • A. El KhalilDepartment of Mathematics
    Faculty of Sciences
    Al-Imam Muhammad ibn Saud Islamic University
    P.O. Box 90950
    Riyadh 11623, Saudi Arabia
    e-mail
  • S. El ManouniDepartment of Mathematics
    Faculty of Sciences
    Al-Imam Muhammad ibn Saud Islamic University
    P.O. Box 90950
    Riyadh 11623, Saudi Arabia
    e-mail
  • M. OuananDépartement d'Informatique
    Faculté des Sciences
    et Techniques Errachidia (FSTE)
    B.P. 509, Boutalamine
    52000 Errachidia, Morocco
    e-mail

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