Positive solutions for singular semi-positone boundary value problems
Sufficient conditions are given for the existence of at least one positive solution to the boundary value problem \[ -y''(t)= f(t, y)+ q(t),\quad 0< t< 1,\qquad y(0)= y(1)= 0, \] which may be singular at \(t= 0\), \(t= 1\), \(y= 0\). For \(0< t< 1\), \(y> 0\), it is assumed that the function \(f(t,y)\) is continuous and positive, and the function \(q(t)\) is continuous and may change sign. The theorem is illustrated by an equation with \(t^{-1/2}\) and \(y^{-2}\) in the right-hand side.
singular nonlinear boundary value problems
scientific article; zbMATH DE number 1866579