Nontrivial solutions of systems of Hammerstein integral equations with first derivative dependence

By means of classical fixed point index, we prove new results on the existence, non-existence, localization and multiplicity of nontrivial solutions for systems of Hammerstein integral equations where the nonlinearities are allowed to depend on the first derivative. As a byproduct of our theory we discuss the existence of positive solutions of a system of third order ODEs subject to nonlocal boundary conditions. Some examples are provided in order to illustrate the applicability of the theoretical results.Comment: 18 page

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

On the solvability of third-order three point systems of differential equations with dependence on the first derivative

This paper presents sufficient conditions for the solvability of the third order three point boundary value problem \begin{equation*} \left\{ \begin{array}{c} -u^{\prime \prime \prime }(t)=f(t,\,v(t),\,v^{\prime }(t)) \\ -v^{\prime \prime \prime }(t)=h(t,\,u(t),\,u^{\prime }(t)) \\ u(0)=u^{\prime }(0)=0,u^{\prime }(1)=\alpha u^{\prime }(\eta ) \\ v(0)=v^{\prime }(0)=0,v^{\prime }(1)=\alpha v^{\prime }(\eta ). \end{array} \right. \end{equation*} The arguments apply Green's function associated to the linear problem and the Guo--Krasnosel'ski\u{\i} theorem of compression-expansion cones. The dependence on the first derivatives is overcome by the construction of an adequate cone and suitable conditions of superlinearity/sublinearity near $0$ and $+\infty .$ Last section contains an example to illustrate the applicability of the theorem.Comment: 21 page

Non-negative solutions of systems of ODEs with coupled boundary conditions

We provide a new existence theory of multiple positive solutions valid for a wide class of systems of boundary value problems that possess a coupling in the boundary conditions. Our conditions are fairly general and cover a large number of situations. The theory is illustrated in details in an example. The approach relies on classical fixed point index

Cointegration and tests of a classical model of inflation in Argentina, Bolivia, Brazil, Mexico, And Peru

Inflation (Finance) - Latin America ; Bolivia ; Argentina ; Inflation (Finance) - Brazil ; Brazil ; Mexico ; Peru

The credibility and performance of unilateral target zones: a comparison of the Mexican and Chilean cases

Foreign exchange rates ; Mexico ; Latin America

EXISTENCE OF EXTREMAL SOLUTIONS FOR SOME FOURTH

In this work we present sufficient conditions for the existence of extremal solutions for some fourth order functional problem with the nonlinearity and boundary functions not necessarily continuous, but satisfying some monotonicity assumptions. The arguments make use of lower and upper solutions technique, a version of Bolzano’s theorem and existence of extremal fixed points for a suitable mapping

Fourth order functional boundary value problems: Existence results and extremal solutions

In this work we present two types of results for some fourth order functional boundary value problems. The first one presents an existence and location result for a problem where every boundary conditions have functional dependence. The second one states sufficient conditions for the existence of extremal solutions for functional problems with more restrict boundary functions. The arguments make use of lower and upper solutions technique, a Nagumo-type condition,an adequate version of Bolzano’s theorem and existence of extremal fixed points for a suitable mapping

Location results: an under used tool in higher order boundary value problems

The method of lower and upper solutions provides, as well as residts of existence, other important properties such as location of solution, extremal solutions,..., which have been under used and, moreover, its potential has not been optimized, either in theory either in applications. This work will present some cases to emphasize both items: two fourth order problems with functional boundary conditions (including an application to a continuous model for the deformation of the human spine under the action of some forces) and a third order periodic problem where unbounded nonlinearities are allowed, provided that an one-sided Nagumo-type condition is verified