A Role of Abel's Equation in the Stabitity Theory of Differential Equations
A simple boundedness theorem for a Liénard equation with damping
A simple model of thermoelectric oscillations
A system of ordinary differential equations modelling an electric circuit with a thermistor is considered. Qualitative properties of solution are studied, in particular, the existence and nonexistence of time-periodic solutions (the Hopf bifurcation).
A singular perturbation method for saddle connections and subharmonics of certain nonlinear differential equations with fixed saddle points.
Saddle connections and subharmonics are investigated for a class of forced second order differential equations which have a fixed saddle point. In these equations, which have linear damping and a nonlinear restoring term, the amplitude of the forcing term depends on displacement in the system. Saddle connections are significant in nonlinear systems since their appearance signals a homoclinic bifurcation. The approach uses a singular perturbation method which has a fairly broad application to saddle...
A smooth Lyapunov function from a class- estimate involving two positive semidefinite functions
A smooth Lyapunov function from a class- estimate involving two positive semidefinite functions
We consider differential inclusions where a positive semidefinite function of the solutions satisfies a class- estimate in terms of time and a second positive semidefinite function of the initial condition. We show that a smooth converse Lyapunov function, i.e., one whose derivative along solutions can be used to establish the class- estimate, exists if and only if the class- estimate is robust, i.e., it holds for a larger, perturbed differential inclusion. It remains an open question whether...
A solution of the continuous Lyapunov equation by means of power series
A solution to the bidimensional global asymptotic stability conjecture
A spectral mapping theorem for semigroups solving PDEs with nonautonomous past.
A stability criterion for periodic systems with first integrals
A stability theory for perturbed differential equations.
A sufficient condition for a system of ordinary differential equations to be technically contractively stable.
A Theorem on Average Liapunov Functions.
A theorem on the structural stability of non-autonomous differential equations
A three-species food chain system with two types of functional responses.
A Tikhonov-type theorem for abstract parabolic differential inclusions in Banach spaces
We consider a class of singularly perturbed systems of semilinear parabolic differential inclusions in infinite dimensional spaces. For such a class we prove a Tikhonov-type theorem for a suitably defined subset of the set of all solutions for ε ≥ 0, where ε is the perturbation parameter. Specifically, assuming the existence of a Lipschitz selector of the involved multivalued maps we can define a nonempty subset of the solution set of the singularly perturbed system. This subset is the set of...
A two-dimensional model for the transmission of dengue fever disease.
A useful proposition to nonlinear differential systems with a solution of the prescribed asymptotic properties
A weak invariance principle and asymptotic stability for evolution equations with bounded generators.
A within-host dengue infection model with immune response and nonlinear incidence rate
A model of viral infection of monocytes population by the dengue virus is formulated as a system of four ordinary differential equations. The model takes into account the immune response and nonlinear incidence rate of susceptible and free virus particles. Global stability of the uninfected steady state is investigated. Such a steady state always exists. If it is the only steady state, then it is globally asymptotically stable. If any infected steady state exists, then the uninfected...