Existence of solutions for some nonlinear singular boundary value problems (Q1821239)

The authors consider the question of existence of solutions to the following boundary value problem \(Lu=f(t,u,pu')\) on (0,1) in which \(Lu\equiv (1/q(t))(p(t)u'(t))'\) with \(u(1)=0\). The boundary conditions at \(t=0\) are to be determined according to the behaviour of p(t) near \(t=0\). Among the other conditions, it is assumed that p,q\(\in C[0,1]\cap C'[0,1]\) with \(p,q>0\) on (0,1] and \(p(0)=0\).