Abstract: In a previous paper we introduced various definitions of stability and instability for non-autonomous differential equations, and applied these to investigate the bifurcations in some simple models. In this paper we present a more systematic theory of local bifurcations in scalar non-autonomous equations. [Copyright &y& Elsevier]
Abstract: In this paper we are interested in establishing up-to boundary uniform estimates for the one phase singular perturbation problem involving a nonlinear singular/degenerate elliptic operator. Our main result states: if is a domain, for some and verifies where , and with some positive constants B and M, then there exists a constant independent of ε such that . [Copyright &y& Elsevier]
Abstract: The problem of a classification of robust homoclinic cycles in low-dimensional spaces has been frequently asked in recent years. In this paper, we resume the results in and and we solve the problem in in the case of orientation-preserving group actions. [Copyright &y& Elsevier]