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

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.

Show me the PDF file (380 KB), TEX file, and other files for this article.

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

Return to the EJDE web page