Positive solution for a class of second-order nonlinear boundary value problems (Q2735476)

The author considers the existence of positive solutions to the nonlinear boundary value problem NEWLINE\[NEWLINE{1\over p} (py')'+ \varphi(t) f(t,y,py')= 0,\quad 0< t< 1,\quad y(0)= \lim_{t\to 1^-} p(t) y'(t)= 0,NEWLINE\]NEWLINE where \(p\in C[0,1]\cap C^1(0,1)\) with \(p(t)> 0\) on \((0,1)\), \(\varphi\in C(0,1)\) with \(\varphi(t)> 0\) on \((0,1)\), \(f\) is singular at \(py'= 0\) but not at \(y= 0\). The proofs are based on the nonlinear alternative.