The critical hyperbola for a Hamiltonian elliptic system with weights期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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The critical hyperbola for a Hamiltonian elliptic system with weights

Authors:

Djairo G de Figueiredo Ireneo Peral Julio D Rossi

Institution:

(1) IMECC, Universidade Estadual de Campinas, 13081-970 Campinas, SP, Brazil;(2) Departamento de Matemáticas, U. Autonoma de Madrid, 28049 Madrid, Spain;(3) Departamento de Matemática, FCEyN, UBA (1428), Buenos Aires, Argentina

Abstract:

In this paper we look for existence results for nontrivial solutions to the system,

$\left\{\begin{array}{ll} \displaystyle -\Delta u = \frac{v^p}{|x|^\alpha} & \quad \mbox{in } \Omega,\\5mm] \displaystyle - \Delta v = \frac{u^q}{|x|^\beta}& \quad \mbox{in } \Omega, \end{array}\right.$

with Dirichlet boundary conditions, u = v = 0 on $\partial \Omega$ 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.

Keywords:

Elliptic systems Nonlinear boundary conditions Variational problems

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