Global Structure of Positive Solutions for a Singular Fourth-Order Integral Boundary Value Problem

摘要

We consider fourth-order boundary value problems u'''' (t) = λh(t)f(u(t)), 0 < t< 1, u(0) = ∫_0~1 u(s)dα(s), u'(0) = u(1) = u'(1) = 0, where ∫_0~1 u(s)dα(s) is a Stieltjes integral with α(t) being nondecraeasing and α(t) being not a constant on [0,1];h(t) may be singular at t = 0 and t=1,h ? C((0,1), [0,∞)) with | h(t) ≠ 0 on any subinterval of (0,1); f ? C([0,∞)) and f(s)> 0 for all s > 0, and f_0 = ∞, f_∞= 0, f_0 = lim(s→0+) f(s)/s, f_∞ = lim_(s→+∞)f(s)/s. We investigate the global structure of positive solutions by using global bifurcation techniques.