Browsing by Author "Biset, Tesfa"

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    A Singular Boundary Value Problem for a Degenerate Elliptic Partial Differential Equation
    (Addis Ababa University, 2015-06) Biset, Tesfa; Mohammed, Seid (PhD)
    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