The existence of non-trivial periodic solutions of a general family of second order differential equations whose main model is a Hill’s equation with a cubic nonlinear term arising in different physical applications is proved. c © 2005 Elsevier Ltd. All rights reserved.

We reanalyze the gravitating monopole and its black hole solutions in the EinsteinYang-Mills-Higgs system and we discuss their stabilities from the point of view of catastrophe theory. Although these non-trivial solutions exhibit fine and complicated structures, we find that stability is systematically understood via a swallow tail catastrophe. The Reissner-Nordström trivial solution becomes un...

We classify all bifurcations from traveling waves to non-trivial time-periodic solutions of the Benjamin-Ono equation that are predicted by linearization. We use a spectrally accurate numerical continuation method to study several paths of non-trivial solutions beyond the realm of linear theory. These paths are found to either re-connect with a different traveling wave or to blow up. In the lat...

A non-trivial solution of (1) is called oscillatory if for every N > 0 there exists an n > N such that X,X n + , 6 0. If one non-trivial solution of (1) is oscillatory then, by virtue of Sturm’s separation theorem for difference equations (see, e.g., [S]), all non-trivial solutions are oscillatory, so, in studying the question of whether a solution {x,> of (1) is oscillatory, it is no restricti...

Were all authors at both of their affiliations when the paper was written or are any of these present addresses? In this paper we study a non-homogeneous Neumann-type problem which involves a nonlinearity satisfying a non-standard growth condition. By using a recent Change OK? variational principle of Ricceri, we establish the existence of at least two non-trivial solutions in an appropriate Or...

Abstract. This paper concerns the asymptotic behaviour of solutions of functional differential equations with unbounded delay to non–equilibrium limits. The underlying deterministic equation is presumed to be a linear Volterra integro–differential equation whose solution tends to a non–trivial limit. We show when the noise perturbation is bounded by a non–autonomous linear functional with a squ...

A large family of linear, usually overdetermined, systems of partial differential equations that admit a multiplication of solutions, i.e, a bilinear and commutative mapping on the solution space, is studied. This family of PDE’s contains the Cauchy–Riemann equations and the cofactor pair systems, included as special cases. The multiplication provides a method for generating, in a pure algebrai...