Geodesic
Asymptotic behaviour of branches for ground states of elliptic systems
Electronic Journal of Differential Equations, Tome 2013 (2013).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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__a68,
     author = {Bobkov, Vladimir and Il'yasov, Yavdat},
     title = {Asymptotic behaviour of branches for ground states of elliptic systems},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2013},
     year = {2013},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2013__2013__a68/}
}
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
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/EJDE_2013__2013__a68/
LA  - en
ID  - EJDE_2013__2013__a68
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
%I mathdoc
%U http://geodesic.mathdoc.fr/item/EJDE_2013__2013__a68/
%G en
%F EJDE_2013__2013__a68
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__a68/