Noureddine Zeddini

Estimates on the Green Function and Existence of Positive Solutions of Nonlinear Singular Elliptic Equations

We establish a 3G-Theorem for the Greens function for an unbounded regular domain D in ℝn(n ≥ 3), with compact boundary. We exploit this result to introduce a new class of potentials K(D) that properly contains the classical Kato class . Next, we study the existence and the uniqueness of a positive continuous solution u in of the following nonlinear singular elliptic problem where φ is a nonnegative Borel measurable function in D × (0, ∞), that belongs to a convex cone which contains, in particular, all functions φ(x, t) = q(x)t-σ, σ ≥ 0 with q ∈ K(D). We give also some estimates on the solution u.

LARGE AND BOUNDED SOLUTIONS FOR A CLASS OF NONLINEAR SCHRÖDINGER STATIONARY SYSTEMS

In the present paper, we are concerned with entire radially symmetric solutions of nonlinear Schrodinger elliptic systems in anisotropic media. In terms of the growth of the variable potential functions, we establish conditions such that the solutions are either bounded or blow up at infinity.

On the existence of positive solutions for a class of semilinear elliptic equations

We prove some existence and nonexistence results for the semilinear elliptic equation Δu = q(x)f(u) on Ω ⊆ Rn (n ≥ 2) where u is required to blow up on the boundary of Ω and f is a nonnegative function which is assumed to be Lipschitz continuous and bounded away from zero on each interval [e, ∞) and have at worst linear growth.In particular, we extend some results already obtained in the case where f(u)=uγ, 0 > γ ≤ 1.

Existence and Exact Asymptotic Behavior of Positive Solutions for a Fractional Boundary Value Problem

We establish the existence and uniqueness of a positive solution for the fractional boundary value problem , with the condition , where , and is a nonnegative continuous function on that may be singular at or .

Existence and Estimates of Positive Solutions for Some Singular Fractional Boundary Value Problems

We establish the existence and uniqueness of a positive solution for the following fractional boundary value problem, with the conditions , , where , , and is a nonnegative continuous function on that may be singular at or . We also give the global behavior of such a solution.

ESTIMATES ON THE GREEN FUNCTION AND EXISTENCE OF POSITIVE SOLUTIONS FOR SOME NONLINEAR POLYHARMONIC PROBLEMS OUTSIDE THE UNIT BALL

Let be the Green function of (-Δ)m, m ≥ 1, on the complementary D of the unit closed ball in ℝn, n ≥ 2, with Dirichlet boundary conditions , 0 ≤ j ≤ m - 1. We establish some estimates on including the 3G-Inequality given by (1.3). Next, we introduce a polyharmonic Kato class of functions and we exploit the properties of this class to study the existence of positive solutions of some polyharmonic nonlinear elliptic problems.

Positive solutions for some competitive elliptic systems

Using some potential theory tools and the Schauder fixed point theorem, we prove the existence of positive bounded continuous solutions with a precise global behavior for the semilinear elliptic system Δu = p(x)uανr in domains D of ℝn, n ≥ 3, with compact boundary (bounded or unbounded) subject to some Dirichlet conditions, where α ≥ 1, β ≥ 1, r ≥ 0, s ≥ 0 and the potentials p, q are nonnegative and belong to the Kato class K(D).

Positive Solutions for Some Competitive Fractional Systems in Bounded Domains

Using some potential theory tools and the Schauder fixed point theorem, we prove the existence and precise global behavior of positive continuous solutions for the competitive fractional system , in a bounded -domain in , subject to some Dirichlet conditions, where , The potential functions are nonnegative and required to satisfy some adequate hypotheses related to the Kato class of functions .