Electron. J. Diff. Equ., Vol. 2013 (2013), No. 212, pp. 1-21.

Asymptotic behaviour of branches for ground states of elliptic systems

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 $(\lambda, \mu)$. 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.

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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