Existence of Homoclinic Solutions for Nonlinear Second-Order Problems

In this work, we consider the second-order discontinuous equation in the real line, u′′(t)−ku(t)=f(t,u(t),u′(t)),a.e.t∈R, with k>0 and f:R3→R an L1 -Carathéodory function. The existence of homoclinic solutions in presence of not necessarily ordered lower and upper solutions is proved, without periodicity assumptions or asymptotic conditions. Some applications to Duffing-like equations are presented in last section.

UT Austin | Portugal Workshop on Nonlinear Mechanics and Applications in Life Sciences

This is a CoLab Workshop organized as an initiative of the UT Austin | Portugal Program to reinforce the Portuguese competences in Nonlinear Mechanics and in complex problems arising from applications to the mathematical modeling and simulations in the Life Sciences. The Workshop provides a place to exchange recent developments, discoveries and progresses in this challenging research field. The main goal is to bring together doctoral candidates, postdoctoral scientists and graduates interested in the field, giving them the opportunity to make scientific interactions and new connections with established experts in the interdisciplinary topics covered by the event. Another important goal of the Workshop is to promote collaboration between members of the different areas of the UT Austin | Portugal community.