Said El Manouni

On singular quasi-monotone ( p, q )-Laplacian systems

We combine the sub- and supersolution method and perturbation arguments to obtain positive solutions of singular quasi-monotone ( p, q )-Laplacian systems.

Simplicity and stability of the first eigenvalue of a nonlinear elliptic system

We prove some properties of the first eigenvalue for the elliptic system −Δpu=λ|u|α|v|βv in Ω, −Δqv=λ|u|α|v|βu in Ω, (u,v)∈W01,p(Ω)×W01,q(Ω). In particular, the first eigenvalue is shown to be simple. Moreover, the stability with respect to (p,q) is established.

Nonlinear parabolic boundary value problems of infinite order

In this paper an existence result is presented for solution of a parabolic boundary value problem under Dirichlet null boundary conditions for a class of general equations of infinite order with strongly nonlinear perturbation terms.

On the Principal Eigencurve of the p-Laplacian: Stability Phenomena

We show that each point of the principal eigencurve of the nonlinear problem −�pu − �m(x)|u| p 2 u = µ|u| p 2 u in ,

Parabolic Equations of Infinite Order with Data

We prove an existence result of a nonlinear parabolic equation under Dirichlet null boundary conditions in Sobolev spaces of infinite order, where the second member belongs to .

Multiplicity results of p(x)-Laplacian systems with Neumann conditions

In this paper, we study a Neumann problem for elliptic systems with variable exponents. We obtain the existence of at least three nontrivial solutions by using an equivalent variational approach to a recent Ricceri’s three critical points theorem (Ricceri in Nonlinear Anal TMA 70:3084–3089, 2009).

Multiple non-trivial solutions of the Neumann problem for p-Laplacian systems

We obtain multiple non-trivial solutions of the Neumann problem for p-Laplacian systems using Morse theory.

Existence and Nonexistence Results for a Class of Quasilinear Elliptic Systems

Using variational methods, we prove the existence and nonexistence of positive solutions for a class of-Laplacian systems with a parameter.