Uniqueness Theorems for a Singular Partial Differential Equation

Abstract

A singular partial differential equation which occurs frequently in mathematical physics is given bywhere is the Laplacian operator on Rn of which the generic point is denoted by x = (x1, … , xn) and s and k are real numbers. The study of solutions of this equation for the case k = 0 was initiated by A. Weinstein [5], who named it ‘Generalized Axially Symmetric Potential Theory'. Numerous references to the literature on this equation can be found in [1; 3; 6]. The analytic theory of equations of the type mentioned above has extensively been treated in [2].