arXiv subjects

Robert de Sousa

Publications and source records attributed to Robert de Sousa.

3 recordsLinked to original sources

arXiv2020

Heteroclinic and homoclinic solutions for nonlinear second-order coupled systems with phi-Laplacians

In this paper we present sufficient conditions for the existence of heteroclinic or homoclinic solutions for second order coupled systems of differential equations on the real line. We point out that it is required only conditions on the homeomorphisms and no growth or asymptotic conditions are assumed on the nonlinearities. The arguments make use of the fixed point theory, L^1-Carathéodory functions and Schauder's fixed point theorem. An application to a family of second order nonlinear coupled systems of two degrees of freedom, shows the applicability of the main theorem.

math.DS↗

arXiv2017

Existence result for impulsive coupled systems on the half-line

This work considers a second order impulsive coupled system of differential equations with generalized jump conditions in half-line, which can depend on the impulses of the unknown functions and their first derivatives. The arguments apply the fixed point theory, Green's functions technique, L^11-Carathéodory functions and sequences and Schauder's fixed point theorem. The method is based on Carathéodory concept of functions and sequences, together with the equiconvergence on infinity and on each impulsive moment, and it allows to consider coupled fully nonlinearities and very general impulsive functions.

math.CA↗

arXiv2016

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)=αu^{\prime }(η) \\ v(0)=v^{\prime }(0)=0,v^{\prime }(1)=αv^{\prime }(η). \end{array} \right. \end{equation*} The arguments apply Green's function associated to the linear problem and the Guo--Krasnosel'ski\uı 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.

math.CA↗