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The boundary value problem
is studied with a view to obtaining the existence of positive solutions in C1([0, 1])∩C2((0, 1)). The function f is assumed to be singular in the second variable, with the singularity modeled after the special case f(x, y) = a(x)y−p, p>0.
This boundary value problem arises in the search of positive radially symmetric solutions to
where Ω is the open unit ball in ℝN, centered at the origin, Γ is its boundary and |x| is the Euclidean norm of x.
The density u(x, t) of an ideal gas flowing through a homogeneous porous media satisfies the equation 
Here m > 1 is a physical constant and u also satisfies the initial condition 
If the initial data is not strictly positive it is necessary to work with generalized solutions of the Cauchy problem (1), (2) (see [1]). By a weak solution we shall mean a function u(x, t) such that for 
(in the sense of distributions) and 
