Multiple monotone positive solutions for higher order differential equations with integral boundary conditions

where n ≥ , f : [, ]× (R+)n– → R+ is continuous in which R+ = [,+∞), A and B are right continuous on [, ), left continuous at t = , and nondecreasing on [, ], withA() = B() = ; ∫   v(s)dA(s) and ∫   v(s)dB(s) denote the Riemann-Stieltjes integrals of v with respect to A and B, respectively. Boundary value problems (BVPs for short) for nonlinear differential equations arise in many areas of applied mathematics and physics. Many authors have discussed the existence of positive solutions for second order or higher order differential equations with