Geodesic
Asymptotic behaviour of branches for ground states of elliptic systems
Electronic journal of differential equations, Tome 2013 (2013)
We consider the behaviour of solutions to a system of homogeneous equations with indefinite nonlinearity depending on two parameters $(\lambda, \mu)$. Using spectral analysis a critical point $(\lambda^*, \mu^*)$ of the Nehari manifolds and fibering methods is introduced. We study a branch of a ground state and its asymptotic behaviour, including the blow-up phenomenon at $(\lambda^*, \mu^*)$. The differences in the behaviour of similar branches of solutions for the prototype scalar equations are discussed.
Classification : 35J50, 35J55, 35J60, 35J70, 35R05
Keywords: system of elliptic equations, p-Laplacian, indefinite nonlinearity, Nehari manifold, fibering method 
@article{EJDE_2013__2013__a168,
     author = {Bobkov,  Vladimir and Il'yasov,  Yavdat},
     title = {Asymptotic behaviour of branches for ground states of elliptic systems},
     journal = {Electronic journal of differential equations},
     year = {2013},
     volume = {2013},
     zbl = {1290.35081},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2013__2013__a168/}
}
TY  - JOUR
AU  - Bobkov,  Vladimir
AU  - Il'yasov,  Yavdat
TI  - Asymptotic behaviour of branches for ground states of elliptic systems
JO  - Electronic journal of differential equations
PY  - 2013
VL  - 2013
UR  - http://geodesic.mathdoc.fr/item/EJDE_2013__2013__a168/
LA  - en
ID  - EJDE_2013__2013__a168
ER  - 
%0 Journal Article
%A Bobkov,  Vladimir
%A Il'yasov,  Yavdat
%T Asymptotic behaviour of branches for ground states of elliptic systems
%J Electronic journal of differential equations
%D 2013
%V 2013
%U http://geodesic.mathdoc.fr/item/EJDE_2013__2013__a168/
%G en
%F EJDE_2013__2013__a168
Bobkov,  Vladimir; Il'yasov,  Yavdat. Asymptotic behaviour of branches for ground states of elliptic systems. Electronic journal of differential equations, Tome 2013 (2013). http://geodesic.mathdoc.fr/item/EJDE_2013__2013__a168/