- Tytuł:
- Existence of positive continuous weak solutions for some semilinear elliptic eigenvalue problems
- Autorzy:
-
Zeddini, Noureddine
Sari, Rehab Saeed - Powiązania:
- https://bibliotekanauki.pl/articles/2216186.pdf
- Data publikacji:
- 2022
- Wydawca:
- Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
- Tematy:
-
Green function
Kato class
nonlinear elliptic systems
positive solution
maximum principle
Schauder fixed point theorem - 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 $K(D)$.
- Źródło:
-
Opuscula Mathematica; 2022, 42, 3; 489-519
1232-9274
2300-6919 - Pojawia się w:
- Opuscula Mathematica
- Dostawca treści:
- Biblioteka Nauki
Artykuł