Anane Aomar

Publications (13)0 Total impact

• Article: Regularity of the solutions to a nonlinear boundary problem with indefinite weight

  Anane Aomar, Chakrone Omar, Moradi Najat
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  ABSTRACT: In this paper we study the regularity of the solutions to the problemDelta_p u = |u|^{p−2}u in the bounded smooth domainOmega ⊂ R^N,with|∇u|^{p−2} partial_{nu} u = lambda V (x)|u|^{p−2}u + h as a nonlinear boundary condition, where partial Omega is C^{2,beta}, with beta ∈]0, 1[, and V is a weight in L^s(partial Omega) and h ∈ L^s(partial Omega ) for some s ≥ 1. We prove that all solutions are in L^{infty}(Omega) cap L^{infty}(Omega), and using the D.Debenedetto’s theorem of regularity in [1] we conclude that those solutions are in C^{1,alpha} overline{Omega}) for some alpha ∈ ]0, 1[.
  Boletim da Sociedade Paranaense de Matemática. 01/2011;
• Article: A non resonance under and between the two first eigenvalues in a nonlinear boundary problem

  Anane Aomar, Chakrone Omar, Moradi Najat
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  ABSTRACT: In this paper we study the non resonance of solutions under andbetween the two first eigenvalues for the problem∆_p u = |u|^{p−2} u in Ω|∇u|^{p−2} ∂ν u= f (x,u) on ∂Ω.
  Boletim da Sociedade Paranaense de Matemática. 01/2010;
• Article: Eigenvalues of an Operator Homogeneous at the Infinity

  Anane Aomar, Chakrone Omar, Filali Mohammed, Karim Belhadj
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  ABSTRACT: In this paper, we show the existence of a sequences of eigenvalues for an operator homogenous at the infinity, we give his variational formulation and we establish the simplicity of all eigenvalues in the case N = 1. Finally we study thesolvability of the problemA(u) := −div(A(x,∇u)) = f(x, u) + h in Ω,u = 0 on ∂Ω,as well as the spectrum ofG_0'(u) = λm|u|^{p−2}u in Ω,u = 0 on ∂Ω.
  Boletim da Sociedade Paranaense de Matemática. 01/2010;
• Article: Existence for an elliptic system with nonlinear boundary conditions

  Anane Aomar, Chakrone Omar, Karim Belhadj, Zerouali Abdellah
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  ABSTRACT: In this paper we prove the existence of a weak solution to the following system△_p u = △_q v = 0 in Ω,|∇u|^{p−2} ∂_ν u = f(x,u) − (α + 1)K(x)|u|^{α−1}u|v|^{β+1} + f1 on ∂Ω,|∇v|^{q−2} ∂_ν v = g(x,v) − (β + 1)K(x)|v|^{β−1}v|u|^{α+1} + g1 on ∂Ω,where Ω is a bounded domain in RN (N ≥ 2), f1, g1, f, g and K are functions that satisfy some conditions.
  Boletim da Sociedade Paranaense de Matemática. 01/2010;
• Source

  Available from: sanu.ac.rs

  Article: Lienard type p-Laplacian neutral Rayleigh equation with a deviating argument

  Anane Aomar, Chakrone Omar, Moutaouekkil Loubna
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  ABSTRACT: Based on Manasevich-Mawhin continuation theorem, we prove the existence of periodic solutions for Lienard type $p$-Laplacian neutral Rayleigh equations with a deviating argument, $$ (phi_p(x(t)-c x(t-sigma))')'+f(x(t))x'(t)+ g(t,x(t-au(t)))=e(t). $$ An example is provided to illustrate our results.
  Electronic Journal of Differential Equations. 01/2010;
• Article: The beginning of the Fucik spectrum for a Steklov Problem

  Anane Aomar, Chakrone Omar, Karim Belhadj, Zerouali Abdellah
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  ABSTRACT: abstract: In this paper, we give some properties of the first nonprincipal eigenvalue for an asymmetric Steklov problem with weights, and we study the Fucik spectrum.
  Boletim da Sociedade Paranaense de Matemática. 01/2009;
• Article: Existence of solutions for a resonant Steklov Problem

  Anane Aomar, Chakrone Omar, Karim Belhadj, Zerouali Abdellah
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  ABSTRACT: In this paper, we prove the existence of weak solutions to the problem△_p u = 0 in Ω, |∇u|^{p−2} ∂_ν u = λ_1 m(x)|u|^{p−2}u + f(x, u) − h on ∂Ω, where Ω is a bounded domain in RN (N ≥ 2), m ∈ L^q(∂Ω) is a weight, λ_1 is the first positive eigenvalue for the eigenvalue Steklov problem △pu = 0 in Ω and |∇u|^{p−2} ∂_ν u=λ m(x)|u|^{p−2}u on ∂Ω. f and h are functions that satisfy some conditions.
  Boletim da Sociedade Paranaense de Matemática. 01/2009;
• Source

  Available from: nsc.ru

  Article: Eigencurves for a Steklov problem

  Anane Aomar, Chakrone Omar, Karim Belhadj, Zerouali Abdellah
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  ABSTRACT: In this article, we study the existence of the eigencurves for a Steklov problem and we obtain their variational formulation. Also we prove the simplicity and the isolation results of each point of the principal eigencurve. Also we obtain the continuity and the differentiability of the principal eigencurve.
  Electronic Journal of Differential Equations. 01/2009;
• Source

  Available from: ub.edu

  Article: On a problem of lower limit in the study of nonresonance with Leray-Lions operator

  Anane Aomar, Chakrone Omar, Chehabi Mohammed
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  ABSTRACT: We prove the solvability of the Dirichlet problem $$displaylines{ Au = f(u)+h quadext{in } Omega , cr u = 0 quadext{on }partial Omega }$$ for a given $h$, under a condition involving only the asymptotic behaviour of the potential $F$ of $f$, where $A$ is a Leray-Lions operator.
  Electronic Journal of Differential Equations. 01/2006;
• Source

  Available from: impa.br

  Article: Nonresonance conditions for a semilinear wave equation in one space dimension

  Anane Aomar, Chakrone Omar, Zerouali Abdellah
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  ABSTRACT: In this paper we study the existence of periodic weak solutions for semilinear wave equations in one space dimension in the case of nonresonance.
  Electronic Journal of Differential Equations. 01/2006;
• Source

  Available from: adelaide.edu.au

  Article: Maximum and anti-maximum principles for the p-Laplacian with a nonlinear boundary condition

  Anane Aomar, Chakrone Omar, Moradi Najat
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  ABSTRACT: In this paper we study the maximum and the anti-maximum principles for the problem $Delta _{p}u=|u|^{p-2}u$ in the bounded smooth domain $Omega subset mathbb{R}^{N}$, with $|abla u|^{p-2}frac{partial u}{partial u }=lambda |u|^{p-2}u+h$ as a non linear boundary condition on $partial Omega $ which is supposed $C^{2eta }$ for some $eta $ in $]0,1[$, and where $hin L^{infty }(partial Omega )$. We will also examine the existence and the non existence of the solutions and their signs.
  Electronic Journal of Differential Equations. 01/2006;
• Source

  Available from: ub.edu

  Article: Existence of solutions for some nonlinear elliptic equations

  Anane Aomar, Chakrone Omar, Chehabi Mohammed
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  ABSTRACT: In this paper, we study the existence of solutions to the following nonlinear elliptic problem in a bounded subset $Omega$ of $mathbb{R}^{N}$: $$displaylines{ -Delta _{p}u = f(x,u, abla u)+mu quad hbox{in } Omega ,cr u = 0 quad hbox{on }partial Omega , }$$ where $mu $ is a Radon measure on $Omega $ which is zero on sets of $p$-capacity zero, $f:Omega imes mathbb{R}imes mathbb{R} ^{N}o mathbb{R}$ is a Caratheodory function that satisfies certain conditions with respect to the one dimensional spectrum.
  Electronic Journal of Differential Equations. 01/2006;
• Article: Strongly nonlinear elliptic problem without growth condition

  Anane Aomar, Chakrone Omar
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  ABSTRACT: We study a boundary-value problem for the $p$-Laplacian with a nonlinear term. We assume only coercivity conditions on the potential and do not assume growth condition on the nonlinearity. The coercivity is obtained by using similar non-resonance conditions as those in cite{An-Go}.
  Electronic Journal of Differential Equations. 01/2002;