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Carathéodory theory of nonresonant second order boundary value problems. (English) Zbl 0870.34028
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.
MSC:
 34B15 Nonlinear boundary value problems for ordinary differential equations