The shooting method and positive solutions of fourth-order impulsive differential equations with multi-strip integral boundary conditions

where 0 < αi < βi < 1, 0 < ξi < ηi < 1, γi > 0, ρi > 0, i = 1, 2, . . . ,n, λ > 0, μ > 0. J = [0, 1], J∗ = J\{t1, t2, . . . , tp}, 0 = t0 < t1 < t2 < · · · < tp < tp+1 = 1, u(tk) = u(t+ k ) – u(t– k ) denotes the jump of u(t) at t = tk , u(t+ k ) and u(t – k ) represent the right and left limits of u(t) at t = tk , respectively, u′(tk) has a similar meaning for u′(t). In fact, multi-strip conditions correspond to a linear combination of integrals of unknown function on the sub-intervals of J . The multi-strip conditions appear in the mathematical modelings of the physical phenomena, for instance, see [1, 2]. They have various applications in realistic fields such as blood flow problems, semiconductor problems, hy-