Some new results for second order boundary value problems (Q923185)

The author presents existence results for a variety of two-point boundary value problems for second order differential equations of the form \[ y''\pm f(t,y,y')=0,\quad y''=\phi^ 2f(t,y,y'),\quad 0<t<1, \] where \(\phi^ 2\) is a positive constant, and the nonlinearity f is allowed to be singular at \(y=0\), \(t=0\) and/or \(t=1\). The methods used rely essentially on the topological transversality theorem, based on the notion of an essential map.