scholarly journals The first eigenvalue and eigenfunction of a nonlinear elliptic system

2019 ◽  
Vol 145 ◽  
pp. 159-174
Author(s):  
Farid Bozorgnia ◽  
Seyyed Abbas Mohammadi ◽  
Tomáš Vejchodský
Keyword(s):  
Elliptic System ◽  
Nonlinear Elliptic System ◽  
First Eigenvalue ◽  
The First Eigenvalue ◽  
Nonlinear Elliptic ◽  
Eigenvalue And Eigenfunction

scholarly journals Simplicity and stability of the first eigenvalue of a nonlinear elliptic system

2005 ◽  
Vol 2005 (10) ◽  
pp. 1555-1563 ◽  
Author(s):  
Abdelouahed El Khalil ◽  
Said El Manouni ◽  
Mohammed Ouanan
Keyword(s):  
Elliptic System ◽  
Nonlinear Elliptic System ◽  
First Eigenvalue ◽  
The First Eigenvalue ◽  
Nonlinear Elliptic ◽  
The Stability

We prove some properties of the first eigenvalue for the elliptic system−Δpu=λ|u|α|v|βvinΩ,−Δqv=λ|u|α|v|βuinΩ,(u,v)∈W01,p(Ω)×W01,q(Ω). In particular, the first eigenvalue is shown to be simple. Moreover, the stability with respect to(p,q)is established.

On Some Generalized Compound Problem for a Nonlinear Elliptic System

1986 ◽  
Vol 126 (1) ◽  
pp. 55-62
Author(s):  
J. Wolska-Bochenek ◽  
L. Von Wolfersdorf
Keyword(s):  
Elliptic System ◽  
Nonlinear Elliptic System ◽  
Nonlinear Elliptic

scholarly journals Existence of Nontrivial Solutions for Perturbed Elliptic System inℝN

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Juan Jiang
Keyword(s):  
Variational Method ◽  
Critical Exponent ◽  
Elliptic System ◽  
Existence Result ◽  
Nonlinear Elliptic System ◽  
Nontrivial Solutions ◽  
Nonlinear Elliptic ◽  
Sobolev Critical Exponent

We consider the perturbed nonlinear elliptic system-ε2Δu+V(x)u=K(x)|u|2*-2u+Hu(u,v),  x∈ℝN,-ε2Δv+V(x)v=K(x)|v|2*-2v+Hv(u,v),  x∈ℝN, whereN≥3,2*=2N/(N-2)is the Sobolev critical exponent. Under proper conditions onV,H, andK, the existence result and multiplicity of the system are obtained by using variational method providedεis small enough.

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