Existence of positive solutions for a class of singular two point boundary value problems of second order nonlinear equations (Q1352737)

The author establishes the existence of positive solutions of singular twopoint boundary value problems \[ (|y'|^{p-2}y')'+ f(t,y)=0, \qquad (p>1),\tag{1} \] \[ y(0)= y(1)=0, \quad \text{or}\quad y(0)=0, \quad y'(1)=c\geq 0.\tag{2} \] The function \(f\) is allowed to be singular when \(y=0\). The problem (1), (2) is transformed into an equivalent integral equation \(y=Ny\). Then the Leray-Schauder degree theory is applicable to research this equation.