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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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