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Existence of solutions for a sublinear system of elliptic equations. (English) Zbl 0993.35032
Summary: We study the existence of nontrivial nonnegative solutions for the system \[ -\Delta u = |x|^av^p,\qquad \Delta v = |x|^bu^q, \] where \(p\) and \(q\) are positive constants with \(pq<1\), and the domain is the unit ball of \({\mathbb{R}}^N\) (\(N>2\)) except for the center zero. We look for pairs of functions that satisfy the above system and Dirichlet boundary conditions set to zero. Our results also apply to some super-linear systems.

MSC:
35J55 Systems of elliptic equations, boundary value problems (MSC2000)
35A07 Local existence and uniqueness theorems (PDE) (MSC2000)
35A20 Analyticity in context of PDEs
35J60 Nonlinear elliptic equations
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