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Asymptotic behaviour of branches for ground states of elliptic systems. (English) Zbl 1290.35081
Summary: We consider the behaviour of solutions of 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.

##### MSC:
 35J50 Variational methods for elliptic systems 35B40 Asymptotic behavior of solutions to PDEs 35B44 Blow-up in context of PDEs 35J70 Degenerate elliptic equations 35R05 PDEs with low regular coefficients and/or low regular data
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