Syrine Masmoudi

Combined effects in nonlinear singular elliptic problems in a bounded domain

Abstract. We establish an existence result of positive solutions to the following boundary value problem: where is a bounded -domain in ℝn, and are nonnegative functions in , , satisfying some appropriate assumptions related to Karamata regular variation theory. We give estimates on such solutions where appear the combined effects of singular and sublinear terms in the nonlinearity.

Estimates for the Green function and singular solutions for polyharmonic nonlinear equation

We establish a new form of the 3G theorem for polyharmonic Green function on the unit ball of ℝn(n≥2) corresponding to zero Dirichlet boundary conditions. This enables us to introduce a new class of functions Km,n containing properly the classical Kato class Kn. We exploit properties of functions belonging to Km,n to prove an infinite existence result of singular positive solutions for nonlinear elliptic equation of order 2m.

Existence and Asymptotic Behaviour of Large Solutions of Semilinear Elliptic Equations

In this paper we are interested in the semilinear elliptic equations of the type Δu=u⋅ϕ(⋅,u), on bounded smooth domain Ω of Rn. We also treat existence of positive solution of Δu=p(x)f(u), which explodes near the boundary of Ω (called large solutions). Our approach is based on potential theory.

Sur les Solutions D'un Opérateur Différentiel Singulier Semi-Linéaire

This paper deals with the following Dirichlet problem Lu = 1A ( Au′ − qu = − f ( , u ) on ] 0, ω [ , u, ( 0 ) = 0, u ( ω ) = 0, where ω ɛ ] 0, + ∞ ], q ≤ 0 is continuous on [ 0, ω [ × ] 0, + ∞ [ → ] 0, + ∞ [ is continuous and A satisfies some appropriate conditions. The main result is the existence and the uniqueness of a strictly positive regular solution of the problem ( ✱ ). Moreover, we study the behaviour of this solution in a neighbourhood of ω. Our approach is based on the use of the Greens function of the homogeneous equation and Schauders fixed point theorem.