Temat: Kato class - Prolib Integro

Skocz do pozycji: 1.

Tytuł:: Nonnegative solutions for a class of semipositone nonlinear elliptic equations in bounded domains of $ \mathbb{R}^n $
Autorzy:: Bachar, Imed
Mâagli, Habib
Eltayeb, Hassan
Tematy:: nonnegative solution
semipositone
Kato class
fixed point theorem; Pokaż więcej
Wydawca:: Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Powiązania:: https://bibliotekanauki.pl/articles/29519177.pdf Link otwiera się w nowym oknie
Opis:: 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 $ \mathbb{R}^n $ (n ≥ 2). The global behavior of this solution is also given.
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 2.

Tytuł:: On the existence of positive continuous solutions for some polyharmonic elliptic systems on the half space
Autorzy:: Zine El Abidine, Z.
Tematy:: polyharmonic elliptic system
Green function
Kato class
positive continuous solution
Schauder fixed point theorem; Pokaż więcej
Wydawca:: Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Powiązania:: https://bibliotekanauki.pl/articles/255368.pdf Link otwiera się w nowym oknie
Opis:: 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].
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 3.

Tytuł:: Existence of positive continuous weak solutions for some semilinear elliptic eigenvalue problems
Autorzy:: Zeddini, Noureddine
Sari, Rehab Saeed
Tematy:: Green function
Kato class
nonlinear elliptic systems
positive solution
maximum principle
Schauder fixed point theorem; Pokaż więcej
Wydawca:: Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Powiązania:: https://bibliotekanauki.pl/articles/2216186.pdf Link otwiera się w nowym oknie
Opis:: Let D be a bounded $C^(1,1)$ -domain in $R^d$, 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, $u = ϕ_1$ and $v = ϕ_2$ on $∂D$, where $ϕ_1$ and $ϕ_2$ 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 $f(x, u, v) = p(x)u^(α) h_1 (v)$ and $g(x, u, v) = q(x)h_2 (u)v^β$ with $α ≥ 1$, $β ≥ 1$, $h_1$, $h_2$ are continuous on $[0,∞)$ and $p$, $q$ are nonnegative functions in $K(D)$.
Dostawca treści:: Biblioteka Nauki

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