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Existence of solutions of a nonlocal elliptic system via Galerkin method. (English) Zbl 1242.65236

Summary: By means of the Galerkin method and by using a suitable version of the Brouwer fixed-point theorem, we establish the existence of at least one positive solution of a nonlocal elliptic \(N\)-dimensional system coupled with Dirichlet boundary conditions.

MSC:

65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35J99 Elliptic equations and elliptic systems
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