Multiple positive solutions to singular boundary value problems for superlinear second-order ODEs
The author studies the boundary value problem \[ y''+q(t)f(t,y)= 0,\;0<t<1, \quad y(0)=y(1)=0, \] where \(q(t)\) may be singular at \(t=0\) and \(t=1\), and \(f(t,y)\) may be superlinear at \(y=\infty\) and singular at \(y=0\). Results guaranteeing the existence of multiple positive solutions to this prohlem are obtained. The proofs rely on properties of Green's function and a fixed-point theorem in cones.
scientific article; zbMATH DE number 1810187