Multiple positive solutions for a second-order boundary value problem with integral boundary conditions

where α and β are nonnegative constants. Boundary value problems of ordinary differential equations arise in kinds of different areas of applied mathematics and physics. Many authors have studied two-point, threepoint, multi-point boundary value problems for second-order differential equations extensively, see [–] and the references therein. In recent years, boundary value problems with integral boundary conditions also arise in thermal conduction, chemical engineering, underground water flow, and plasma physics. Some authors have investigated boundary value problems with integral boundary conditions; see [–]. Boucherif [] considered the following problem: ⎧ ⎪⎨