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

Abstract

We consider fourth-order boundary value problemsu′′′′(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 withα(t)being nondecreasing andα(t)being not a constant on[0,1];h(t)may be singular att=0andt=1,h∈C((0,1),[0,∞))withh(t)≢0on any subinterval of(0,1);f∈C([0,∞),[0,∞))andf(s)>0for alls>0, andf0=∞,  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.