Extremal solutions to fourth order discontinuous functional boundary value problems

In this paper, given f a L1-Carathéodory function, it is considered a functional fourth order equation together with the nonlinear functional boundary conditions given by some functions verifying some adequate monotonicity assumptions and are not necessarily continuous. It will be proved an existence and location result in presence of non ordered lower and upper solutions

A positive fixed point theorem with applications to systems of Hammerstein integral equations

We present new criteria on the existence of fixed points that combine some monotonicity assumptions with the classical fixed point index theory. As an illustrative application, we use our theoretical results to prove the existence of positive solutions for systems of nonlinear Hammerstein integral equations. An example is also presented to show the applicability of our results.Comment: 11 page