Upper and lower solutions for problems with singular sign changing nonlinearities and with nonlinear boundary data (Q701330)

Sufficient conditions are obtained for the existence of solutions to the nonlinear singular boundary value problem \[ y''+ q(t) f(t,y)= 0,\quad 0< t< 1,\quad y(0)= y'(1)+ \psi(y(1))= 0. \] The nonlinearity \(f\) is allowed to change sign and to be singular at \(y= 0\). The proposed approach is also applicable to other types of singular boundary value problems. The results are illustrated by a problem arising in nonlinear mechanics (large deflection membrane response of a spherical cap).