A Singular Boundary Value Problem for a Degenerate Elliptic Partial Differential Equation
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Date
2015-06
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Addis Ababa University
Abstract
A singular boundary value problem associated with the 8-Laplace equation having,
in general a non-separable inhomogeneous term is considered. The existence of ground
state solution in viscosity sense to such a problem in bounded domains as well as in the
whole Euclidean space RN, for N ¥ 2 is established. The investigation of the problem
is mainly based on sub-solution and super-solution methods, and existence of principal
eigenfunctions to the eigenvalue of Dirichlet type problem 8ufpx; uq; u ¡ 0 in an
open set
and upxq 0 on B
, corresponding to the 8-Laplace equation.
Keywords: 8-Laplacian, Viscosity solution, Principal eigenvalue, Principal eigenfunction
Description
Keywords
Laplacian, Viscosity Solution, Principal Eigenvalue, Principal Eigenfunction