Potential estimates in nonpotential boundary value problems (Q1594206)

The two-point boundary value problem under consideration reads \[ -y''+ p(t) y'+ q(t)y= f(t,y,y'),\quad y(0)= y(T)= 0, \] where \(p\) is a continuously differentiable function and \(q\), \(f\) are continuous functions. The existence of a classical solution is examined by means of a potential estimate technique. More precisely, the upper and lower estimates of the nonlinearity \(f\) are averaged, provided these estimates are potential. Two related theorems are presented for the scalar case and one for the vector case.