EXISTENCE OF POSITIVE SOLUTIONS FOR SINGULAR P-LAPLACIAN STURM-LIOUVILLE BOUNDARY VALUE PROBLEMS

We prove the existence of positive solutions of the Sturm-Liouville boundary value problem -(r(t)phi(u'))' = lambda g(t)f(t, u), t is an element of(0,1), au(0) - b phi(-1)(r(0))u'(0) = 0, cu(1) +d phi(-1)(r(1))u'(1) = 0, where phi(u') = vertical bar u'vertical bar(p-2)u', p > 1, f : (0, 1) x (0, infinity) -> R satisfies a p-sublinear condition and is allowed to be singular at u = 0 with semipositone structure. Our results extend previously known results in the literature.