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 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

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

Foreign exchange rates ; Mexico ; Latin America

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

Periodic solutions for some fully nonlinear fourth order differential equations

In this paper we present sufficient conditions for the existence of periodic solutions to some nonlinear fourth order boundary value problems u(4)(x) = f(x; u(x); u′(x); u′′(x); u′′′(x)) u(i)(a) = u(i)(b); i = 0; 1; 2; 3; To the best of our knowledge it is the first time where this type of general nonlinearities is considered in fourth order equations with periodic boundary conditions. The difficulties in the odd derivatives are overcome due to the following arguments: the control on the third derivative is done by a Nagumo-type condition and the bounds on the first derivative are obtained by lower and upper solutions, not necessarily ordered. By this technique, not only it is proved the existence of a periodic solution, but also, some qualitative properties of the solution can be obtained

Existence, nonexistence and multiplicity results for some beam equations

This paper studies some fourth order nonlinear fully equations with a parameter s ∈ R, with two point boundary conditions. These problems model several phenomena, such as, a cantilevered beam with a linear relation between the curvature and the shear force at both endpoints. For some values of the real constants, it will be presented an Ambrosetti–Prodi type discussion on s. The arguments used apply lower and upper solutions technique, a priori estimations and topological degree theory

La sociedad del futuro: las tecnologías ubicuas y su impacto en la sociedad

Treball Final de Grau en Publicitat i Relacions Públiques. Codi: PU0932. Curs acadèmic: 2016/2017Pervasive advertisement is presented as a new way of making advertisement that ultimately will shake the world of communication. The latest technological knowledge in computing, the artificial intelligence studies that are being developed and the large amount of devices and sensors will make the future easier to reach a real pervasive daily life. Through the right procedures and all the developments ongoing mentioned above we will create digital ambients that would be able to understand the consumers feelings after watching an advertisement, to adapt to a determined context and respond efficiently any problem presented. This kind of technology presents loads of benefits besides the ones already mentioned on the advertising field, due to the pervasive technology can be applied to any kind of transmission of information so some years from now we might be able to experience a new communicative chapter globally. The true challenge will be on the one hand to adapt the media production industry to this new reality where it will be need a massive effort to accomplish the requirements of this new platforms and pervasive models. It will be necessary to produce all kinds of media products to give service to a real pervasive and personalised advertisement. On the other hand another challenge will be the control and regulation of this new pervasive technologies within the ethic limits what will establish the base to a good relationship between consumers and advertisers.La publicidad ubicua se presenta como la nueva forma de hacer publicidad que revolucionará el mundo de la comunicación publicitaria. Los avances tecnológicos en computación, los estudios en inteligencia artificial y la multiplicación de dispositivos y sensores hace que cada día que pasa sea más fácil alcanzar una presencia ubicua real en la vida cotidiana. Mediante los procesos adecuados y con estudios que se aproximen a la inteligencia artificial se conseguirán crear ambientes digitales que puedan entender e interpretar los sentimientos de las personas, adaptarse a un contexto concreto y puedan responder eficientemente a los problemas presentados. Por supuesto este tipo de tecnología presenta multitud de beneficios además de los mencionados en el terreno publicitario, ya que la tecnología ubicua puede aplicarse a todo tipo de transmisión de información por lo que desde aquí a unos años, podemos estar experimentando un nuevo capítulo comunicativo a nivel mundial. El verdadero reto, será por un lado conseguir adaptar la industria de producción mediática a esas nuevas métricas debido a que aun teniendo la plataforma será necesaria una gran capacidad de creación de contenidos simultanea, un segundo reto será el control de las tecnologías ubicuas dentro de unos límites éticos que establecerán las bases de una buena relación entre consumidores y anunciantes

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

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