Existence and uniqueness theorems for singular anisotropic quasilinear elliptic boundary value problems

On bounded domains Omega subset of R-2 we consider the anisotropic problems u(-a)u(xx) + u(-b)u(yy) = p(x, y) in Omega with a, b > 1 and u = infinity on partial derivative Omega and u(c)u(xx) + u(d)u(yy) + q(x, y) = 0 in Omeg a with c, d greater than or equal to 0 and u = 0 on partial derivative Omeg a. Moreover, we generalize these boundary value problems to space-dimension s n > 2. Under geometric conditions on Omega and monotonicity assumption on 0 < p, q is an element of C-alpha(<(Omega)over bar>) we prove existence an d uniqueness of positive solutions.