Wyniki wyszukiwania - BazTech

1

Nonnegative solutions for a class of semipositone nonlinear elliptic equations in bounded domains of Rn

Bachar Imed, Mâagli Habib, Eltayeb Hassan

Opuscula Mathematica

|

2022

|

Vol. 42, no. 6

793--803

EN

In this paper, we obtain sufficient conditions for the existence of a unique nonnegative continuous solution of semipositone semilinear elliptic problem in bounded domains of Rn (n ≥ 2). The global behavior of this solution is also given.

2

Existence of positive continuous weak solutions for some semilinear elliptic eigenvalue problems

Zeddini Noureddine, Sari Rehab Saeed

Opuscula Mathematica

|

2022

|

Vol. 42, no. 3

489--519

EN

Let D be a bounded C1,1-domain in Rd, d ≥ 2. The aim of this article is twofold. The first goal is to give a new characterization of the Kato class of functions K(D) that was defined by N. Zeddini for d = 2 and by H. Mâagli and M. Zribi for d ≥ 3 and adapted to study some nonlinear elliptic problems in D. The second goal is to prove the existence of positive continuous weak solutions, having the global behavior of the associated homogeneous problem, for sufficiently small values of the nonnegative constants λ and μ to the following system Δu = λf(x, u, v), Δv = μg(x, u, v) in D, u = ϕ1 and v = ϕ2 on ∂D, where ϕ1 and ϕ2 are nontrivial nonnegative continuous functions on ∂D. The functions f and g are nonnegative and belong to a class of functions containing in particular all functions of the type f(x, u, v) = p(x)uαh1(v) and g(x, u, v) = q(x)h2(u)vβ with α ≥ 1, β ≥ 1, h1, h2 are continuous on [0,∞) and p, q are nonnegative functions in K(D).

3

Large versus bounded solutions to sublinear elliptic problems

Damek Ewa, Ghardallou Zeineb

Bulletin of the Polish Academy of Sciences. Mathematics

|

2019

|

Vol. 67, no. 1

69--82

EN

Let L be a second order elliptic operator with smooth coefficients defined on a domain Ω ⸦ Rd (possibly unbounded), d ≥ 3. We study nonnegative continuous solutions u to the equation Lu(x) - φ (x, u(x)) = 0 on Ω, where φ is in the Kato class with respect to the first variable and it grows sublinearly with respect to the second variable. Under fairly general assumptions we prove that if there is a bounded nonzero solution then there is no large solution.

4

On the existence of positive continuous solutions for some polyharmonic elliptic systems on the half space

Zine El Abidine Z.

Opuscula Mathematica

|

2012

|

Vol. 32, no. 1

91-113

EN

We study the existence of positive continuous solutions of the nonlinear polyharmonic system (-Δ)mu + λqg(v) = 0, (-Δ)mv + μpf(u) = 0 in the half space [formula] where m ≥1 and n>2m.The nonlinear term is required to satisfy some conditions related to the Kato class [formula]. Our arguments are based on potential theory tools associated to (-Δ)m and properties of functions belonging to [formula].

5

One-dimensional symmetric stable Feynman-Kac semigroups

Byczkowska H., Byczkowski T.

Probability and Mathematical Statistics

|

2001

|

Vol. 21, Fasc. 2

381--404

EN

We investigate here one-dimensional Feynman-Kac semigroups based on symmetric α-stable processes. We begin with establishing the properties of Green operators of intervals and halflines on functions from the Kato class. Then we provide a sufficient condition for gaugeability of the halfline(−∞, b) and evaluate the critical value β.