EXISTENCE OF POSITIVE SOLUTIONS TO A SYSTEM OF SINGULAR BOUNDARY VALUE PROBLEMS

Existence results for positive solutions of a coupled system of nonlinear singular two point boundary value problems of the type

                                                  −x ′′(t) = p( t ) f(t, y( t ), x′ (t) ),                    t ∈ (0, 1),

                                                  −y ′′(t) = q( t ) g(t, x( t ), y′ (t) ),                   t ∈ (0, 1),

                                                    a₁x(0) − b₁x ′ (0) = x ′ (1) = 0,

                                                    a₂y(0) − b₂y ′ (0) = y ′ (1) = 0,

are established. The nonlinearities f, g : [0, 1] × [0, ∞) × (0, ∞) → [0, ∞) are allowed to be singular at x ′ = 0 and y ′ = 0. The functions p, q ∈ C(0, 1) are positive on (0, 1) and the constants a_i , b_i (i = 1, 2) > 0. An example is included to show the applicability of our result.