Abstract
In this paper we look for existence results for nontrivial solutions to the system, \( \left\{ {\begin{array}{*{20}c} { - \Updelta u = \frac{{v^{p} }}{{\left| x \right|^{\alpha } }}} & {{\text{in}}\,\Upomega ,} \\ { - \Updelta v = \frac{{u^{p} }}{{\left| x \right|^{\beta } }}} & {{\text{in}}\,\Upomega ,} \\ \end{array} } \right. \) with Dirichlet boundary conditions, u = v = 0 on ∂Ω and α, β < N. We find the existence of a critical hyperbola in the (p, q) plane (depending on α, β and N) below which there exists nontrivial solutions. For the proof we use a variational argument (a linking theorem).
I. Peral was partially supported by project MTM2004-02223 of MEC, Spain. J. D. Rossi partially supported by Universidad de Buenos Aires (grant TX066), ANPCyT and Fundacion Antorchas.
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de Figueiredo, D.G., Peral, I., Rossi, J.D. (2007). The Critical Hyperbola for a Hamiltonian Elliptic System with Weights. In: Costa, D. (eds) Djairo G. de Figueiredo - Selected Papers. Springer, Cham. https://doi.org/10.1007/978-3-319-02856-9_42
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