Global Structure of Positive Solutions for a Singular Fourth-Order Integral Boundary Value Problem - Wenguo Shen; Tao He (Discrete Dynamics in Nature and Society)
We consider fourth-order boundary value problems u′′′′(t)=λh(t)f(u(t)),  0<t<1,  u(0)=∫01‍u(s)dα(s),  u′(0)=u(1)=u′(1)=0, where ∫01‍u(s)dα(s) is a Stieltjes integral with α(t) being nondecreasing 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,∞),[0,∞)) and f(s)>0 for all s>0, and f0=∞,  f∞=0,  f0=lims→0+f(s)/s,  f∞=lims→+∞f(s)/s. We investigate the global structure of positive solutions by using global bifurcation techniques.