A multiplicity result for a singular generalized Sturm–Liouville boundary value problem

Abstract

In this paper, we are concerned with a singular generalized Sturm–Liouville boundary value problem { u ″ ( t ) + h ( t ) f ( t , u ( t ) , u ′ ( t ) ) = 0 , 0 < t < 1 , a u ( 0 ) − b u ′ ( 0 ) = ∑ i = 1 m − 2 a i u ( ξ i ) , c u ( 1 ) + d u ′ ( 1 ) = ∑ i = 1 m − 2 b i u ( ξ i ) , where h may be singular at t = 0 and/or t = 1 . By applying the fixed point theorem in cones, a new and general result on the existence of positive solutions to the second order singular generalized Sturm–Liouville boundary value problem is obtained. The first order derivative is involved in the nonlinear term f explicitly.