Bubble-type solutions of nonlinear singular problems

The paper describes the set of all solutions of the singular initial problems (p(t)u′)′=p(t)f(u),u(0)=B,u′(0)=0, on the half–line [0,∞)[0,∞). Here B<0B<0 is a parameter, p(0)=0p(0)=0 and p′>0p′>0 on (0,∞)(0,∞), f(L)=0f(L)=0 for some L>0L>0 and xf(x)<0xf(x)<0 if x