Existence of solutions to nonlocal and singular elliptic problems via Galerkin method
Date
2004-02-11
Authors
Correa, Francisco Julio S. A.
Menezes, Silvano D. B.
Journal Title
Journal ISSN
Volume Title
Publisher
Southwest Texas State University, Department of Mathematics
Abstract
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.
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.
Description
Keywords
Nonlocal elliptic problems, Galerkin method
Citation
Corrêa, F. J. S. A., & Menezes, S. D. B. (2004). Existence of solutions to nonlocal and singular elliptic problems via Galerkin method. <i>Electronic Journal of Differential Equations, 2004</i>(19), pp. 1-10.
Rights
Attribution 4.0 International