On higher order fully periodic boundary value problems

In this paper we present sufficient conditions for the existence of periodic solutions of some higher order fully differential equation where the nonlinear part verifies a Nagumotype growth condition. A new type of lower and upper solutions, eventually non-ordered, allows us to obtain, not only the existence, but also some qualitative properties on the solution. The last section contains two examples to stress the application to both cases of n odd and n even

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Existence and multiplicity of solutions in fourth order BVPs with unbounded nonlinearities

In this work the authors present some existence, non-existence and location results of the problem composed of a fourth order fully nonlinear equation with a parameter.In this work it is applied an Ambrosetti-Prodi type approach, with some new features: the existence part is obtained in presence of nonlinearities not necessarily bounded, and in the multiplicity result it is not assumed a speed growth condition or an asymptotic condition, as it is usual in the literature for these type of higher order problems. The arguments used apply lower and upper solutions technique and topological degree theory. An application is made to a continuous model of the human spine, used in aircraft ejections, vehicle crash situations, and some forms of scoliosis

Fourth order impulsive periodic boundary value problems

In this work it is presented an existence result for the impulsive problem composed a fourth order fully nonlinear equation, along with periodic boundary conditions and some impulsive conditions u x+j = gj u x j , The arguments used apply lower and upper solutions technique combined with an iterative and non monotone technique

Higher order functional boundary value problems without monotone assumptions

In this paper, given a L1-Carathéodory function f, it is a considered the functional higher order equation, together with nonlinear functional boundary conditions, for. 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

MULTIPLICITY AND LOCATION RESULTS FOR SECOND ORDER FUNCTIONAL BOUNDARY VALUE PROBLEMS

In this work it is presented some existence, non-existence and location results for the problem composed by the second order fully nonlinear equation with a real parameter s and functional boundary conditions satisfying some adequate monotonicity assumptions. It will be done a discussion on s about the existence and non-existence of solutions for problem (E)-(BC): More precisely, there are s0; s1 2 R such that: for s s0) there is no solution of (E)-(BC). for s = s0 problem (E)-(BC) has one solution. The arguments used apply lower and upper solutions technique, a Nagumo condition and a priori estimations

THE ROLE OF LOWER AND UPPER SOLUTIONS IN THE GENERALIZATION OF LIDSTONE PROBLEMS

In this the authors consider a nonlinear fourth order fully equation coupled with the Lidstone boundary conditions, We discuss how di erent de nitions of lower and upper solutions can generalize existence and location results for boundary value problems with Lidstone boundary data. In addition, it is replaced the usual bilateral Nagumo condition by a one-sided condition, allowing the nonlinearity to be unbounded: An example will show that this unilateral condition generalizes the usual one and stress the potentialities of the new de nitions

On the solvability of some fourth-order equations with functional boundary conditions

In this paper it is considered a fourth order problem composed of a fully nonlinear differential equation and functional boundary conditions satisfying some monotone conditions.This functional dependence on u; u0 and u00and generalizes several types of boundary conditions such as Sturm-Liouville, multipoint, maximum and/or minimum arguments, or nonlocal. The main theorem is an existence and location result as it provides not only the existence, but also some qualitative information about the solution

Existence, localization and multiplicity results for nonlinear and functional

In this thesis several problems are addressed. The problems considered vary from second order problems up to high order problems where generaliza- tions to nth order are studied. Such problems range from problems without functional dependence up to problems where the functional dependence is featured both in the equation and on the boundary conditions. Functional boundary conditions include most of the classical conditions as multipoint cases, conditions with delay and/or advances, nonlocal or in- tegral, with maximum or minimum arguments,... Existence, nonexistence, multiplicity and localization results are then discussed in accordance with these conditions. The method used is the lower and upper solutions combined with di¤erent techniques (degree theory, Nagumo condition, iterative technique, Green s function) to obtain such results. Several applications are studied such as the periodic oscillations of the axis of a satellite and conjugate boundary value problems, to emphasize the applicability of the method used; RESUMO:Nesta tese, intitulada em português, Resultados de existência, localiza- ção e multiplicidade para problemas não lineares e funcionais de ordem su- perior com valores na fronteira , diferentes problemas são abordados. Estes problemas variam desde problemas de segunda ordem até problemas de or- dem superior, onde generalizações de ordem n são feitas e onde os problemas apresentados variam desde o caso em que não existe dependência funcional até aos em que esta dependência funcional está presente tanto na equação como nas condições de fronteira. Sobre estas condições, que incluem a maioria das condições clássicas, re- sultados de existência, não existência, multiplicidade e localização de solução são discutidos de acordo com estas condições. O método utilizado é o método da sub e sobre-solução combinado com diferentes técnicas. Várias aplicações são estudadas, nomeadamente as oscilações periódicas do eixo de um satélite e problemas conjugados, de forma a dar ênfase à aplicabilidade do método utilizado

First order coupled systems with functional and periodic boundary conditions: existence results and application to an SIRS model

The results presented in this paper deal with the existence of solutions of a first order fully coupled system of three equations, and they are split in two parts: 1. Case with coupled functional boundary conditions, and 2. Case with periodic boundary conditions. Functional boundary conditions, which are becoming increasingly popular in the literature, as they generalize most of the classical cases and in addition can be used to tackle global conditions, such as maximum or minimum conditions. The arguments used are based on the Arzèla Ascoli theorem and Schauder’s fixed point theorem. The existence results are directly applied to an epidemic SIRS (Susceptible-Infectious-Recovered-Susceptible) model, with global boundary conditions