Positive solutions of singular boundary value problems for systems of nonlinear fourth order differential equations

Abstract

In this paper, we study the singular boundary value problems for systems of nonlinear fourth order differential equations {(u(4)(t) = a1(t) f1(t, u (t), v (t), u″(t), v″(t)) + b1(t) g1(t, u (t), v (t), u″(t), v″(t)),; v(4)(t) = a2(t) f2(t, u (t), v (t), u″(t), v″(t)) + b2(t) g2(t, u (t), v (t), u″(t), v″(t)), 0 < t < 1,; u (0) = u (1) = v (0) = v (1) = 0,; α1u″(0) - β1u‴(0) = 0, γ1u″(1) + δ1u‴(1) = 0,; α2v″(0) - β2v‴(0) = 0, γ2v″(1) + δ2v‴(1) = 0 .) Under some weaker conditions, we show the existence of single and multiple positive solutions of the above problem by applying the fixed-point theorem of cone expansion and compression type due to Krasnosel'skill. © 2007.