We use a direct variational method in order to investigate the dependence on parameter for the solution for a Duffing type equation with Dirichlet boundary value conditions. Mathematics Subject Classification. 49J02

In this paper, we investigate the chaotic behavior of ordinary differential equations with a homoclinic orbit to a dissipative saddle point under an unbounded random forcing driven by a Brownian motion. We prove that, for almost all sample pathes of the Brownian motion in the classical Wiener space, the forced equation admits a topological horseshoe of infinitely many branches. This result is t...

Physical Phenomena’s located around us are primarily nonlinear in nature and their solutions are of highest significance for scientists and engineers. In order to have a better representation of these physical models, fractional calculus is used. Fractional order oscillation equations are included among these nonlinear phenomena’s. To tackle with the nonlinearity arising, in these phenomena’s w...

This brief addresses the robust asymptotic and BIB0(bounded-input bounded-output) stability of a class of linear shift-variant multidimensional systems. Using a shift-invariant comparisonsystem, necessary and sufficient conditions for the stability of the entirefamily of systems are derived.

We consider a second order equation of Duffing type. By applying Mawhin’s continuation theorem and a relationship between the periodic and the Dirichlet boundary value problems for second order ordinary differential equations, we prove that the given equation has at least one positive periodic solution when the singular forces exhibits certain some strong force condition near the origin and wit...

We use the coincidence degree to establish new results on the existence and uniqueness of T -periodic solutions for a kind of Duffing equation with two deviating arguments of the form x ′′ + Cx(t) + g1(t, x(t− τ1(t))) + g2(t, x(t− τ2(t))) = p(t).