Positive Solutions for Second-Order Singular Semipositone Differential Equations Involving Stieltjes Integral Conditions

Abstract

By means of the fixed point theory in cones, we investigate the existence of positive solutions for the following second-order singular differential equations with a negatively perturbed term:−u′′(t)=λ[f(t,u(t))−q(t)],0<t<1,αu(0)−βu′(0)=∫01u(s)dξ(s),γu(1)+δu′(1)=∫01u(s)dη(s),whereλ>0is a parameter;f:(0,1)×(0,∞)→[0,∞)is continuous;f(t,x)may be singular att=0,t=1,andx=0, and the perturbed termq:(0,1)→[0,+∞)is Lebesgue integrable and may have finitely many singularities in(0,1), which implies that the nonlinear term may change sign.