Existence of solutions to nonlocal and singular elliptic problems via Galerkin method
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We study the existence of solutions to the nonlocal elliptic equation -M (||u||2) Δu = ƒ(x, u) with zero Dirichlet boundary conditions on a bounded and smooth domain of ℝn. We consider the M-linear case with ƒ ∈ H-1 (Ω), and the sub-linear case ƒ(u) = uα, 0 < α < 1. Our main tool is the Galerkin method for both cases when M continuous and when M is discontinuous.
CitationCorrêa, F. J. S. A., & Menezes, S. D. B. (2004). Existence of solutions to nonlocal and singular elliptic problems via Galerkin method. Electronic Journal of Differential Equations, 2004(19), pp. 1-10.
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