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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.

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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