Carathéodory theory of nonresonant second order boundary value problems (Q675965)

The author continues to study the solvability of two point singular boundary value problems \((py')'/p+ \tau y+ \sigma py'= f(t,y,py')\) a.e. on \([0,1]\) with \(y\) satisfying Sturm-Liouville, Neumann or periodic boundary conditions. The proofs are based on Leray-Schauder's nonlinear alternative. In order to apply this principle, the author mixes the differential equation, Hölder and Sobolev inequalities and obtains with great art, a-priori bounds of solutions.