Abstract
In this paper, given a -Caratheodory function, it is considered the functional higher order equation together with the nonlinear functional boundary conditions, for Here, , , 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.
Highlights
1 Introduction In this paper, it is considered the functional higher order boundary value problem, for n ≥ composed by the equation u(n)(x) = f x, u,
4 Example This section contains a problem composed by an integro-differential equation with some functional boundary conditions, whose solvability is proved in presence of nonordered lower and upper solutions
Summary
1 Introduction In this paper, it is considered the functional higher order boundary value problem, for n ≥ composed by the equation u(n)(x) = f x, u, . N – , are continuous functions without assuming monotone conditions or another type of variation. Functional boundary value problems have been studied by several authors following several approaches, as it can be seen, for example, in [ – ].
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