Abstract
This paper is devoted to the study of existence of solutions of the nonlinear second-order differential equation u ″( t)+ p( t) u ′( t)+ f( t, u( t))=0 together with different types of linear boundary conditions. To this end we assume the existence of a pair of ordered lower and upper solutions and deduce comparison results for the general linear operator L( p, q) u( t)≡ u ″( t)+ p( t) u ′( t)+ q( t) u( t) together with the condisered boundary conditions.
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