João Fialho

Higher order functional boundary value problems without monotone assumptions

AbstractIn this paper, given f:[a,b]×(C([a,b]))n−2×R2→R a L1-Carathéodory function, it is considered the functional higher order equation u(n)(x)=f(x,u,u′,…,u(n−2)(x),u(n−1)(x)) together with the nonlinear functional boundary conditions, for i=0,…,n−2 Here, Li, i=0,…,n−1, are continuous functions. It will be proved an existence and location result in presence of not necessarily ordered lower and upper solutions, without assuming any monotone properties on the boundary conditions and on the nonlinearity f.