ON A CLASS OF ELLIPTIC SYSTEM OF SCHRÖDINGER–POISSON TYPE

2014 ◽  
Vol 97 (3) ◽  
pp. 301-314
Author(s):  
LUCAS C. F. FERREIRA ◽  
EVERALDO S. MEDEIROS ◽  
MARCELO MONTENEGRO
Keyword(s):  
Elliptic System ◽  
Integral Form ◽  
Nonlinear Elliptic System ◽  
Bessel Potential ◽  
Qualitative Properties ◽  
Nonlinear Elliptic ◽  
The Poisson Equation ◽  
Contraction Map ◽  
Qualitative Properties Of Solutions ◽  
Poisson Type

AbstractIn this paper we prove existence and qualitative properties of solutions for a nonlinear elliptic system arising from the coupling of the nonlinear Schrödinger equation with the Poisson equation. We use a contraction map approach together with estimates of the Bessel potential used to rewrite the system in an integral form.

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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