A Singular Boundary Value Problem For A Degenerate Elliptic Partial Differential Equation

A singular boundary value problem associated with the 8-Laplace equation having,rnin general a non-separable inhomogeneous term is considered. The existence of groundrnstate solution in viscosity sense to such a problem in bounded domains as well as in thernwhole Euclidean space RN, for N ¥ 2 is established. The investigation of the problemrnis mainly based on sub-solution and super-solution methods, and existence of principalrneigenfunctions to the eigenvalue of Dirichlet type problem 8ufpx; uq; u ¡ 0 in anrnopen set rn and upxq 0 on Brn, corresponding to the 8-Laplace equation.rnKeywords: 8-Laplacian, Viscosity solution, Principal eigenvalue, Principal eigenfunction

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