Vladimir Bobkov, Yavdat Il'yasov
Abstract:
We consider the behaviour of solutions to a system of homogeneous
equations with indefinite nonlinearity depending on two parameters
.
Using spectral analysis a critical point
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
.
The differences in the behaviour of similar branches
of solutions for the prototype scalar equations are discussed.
Submitted August 30, 2013. Published September 25, 2013.
Math Subject Classifications: 35J50, 35J55, 35J60, 35J70, 35R05.
Key Words: System of elliptic equations; p-laplacian; indefinite nonlinearity;
Nehari manifold; fibering method.
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Vladimir Bobkov Institute of Mathematics of RAS, Ufa, Russia Ufa State Aviation Technical University, Ufa, Russia email: bobkovve@gmail.com | |
Yavdat Il'yasov Institute of Mathematics of RAS, Ufa, Russia email: ilyasov02@gmail.com |
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