positive solutions for nonlinear systems of third-order generalized sturm-liouville boundary value problems with (p1, p2, . . . , pn)-laplacian

In this work, by employing the Leggett-Williams fixed point theorem, we study the existence of at least three positive solutions of boundary value problems for system of third-order ordinary differential equations with (p1, p2, . . . , pn)-Laplacian  (φpi (u 00 i (t)))0 + ai(t)fi(t, u1(t), u2(t), . . . , un(t)) = 0 0 ≤ t ≤ 1, αiui(0) − βiu 0 i(0) = µi1ui(ξi), γiui(1) + δiu 0 i(1) = µi2ui(ηi), u00 i (0) = 0, where φpi (s) = |s| pi−2 s,, are pi-Laplacian operators, pi > 1, 0 < ξi < 1, 0 < ηi < 1 and µi1, µi2 > 0 for i = 1, 2, . . . , n.