Asymptotic Dichotomy in a Class of Third-Order Nonlinear Differential Equations with Impulses

Solutions of quite a few higher-order delay functional differential equations oscillate or converge to zero. In this paper, we obtain several such dichotomous criteria for a class of third-order nonlinear differential equation with impulses

Oscillation for solutions of nonlinear neutral differential equations with impulses

AbstractThis paper is concerned with nonlinear neutral differential equations with impulses of the form Some oscillation criteria for solutions of this equation are established. An interesting example is also given, which illustrates that impulses play an important role in giving rise to the oscillation of equations

Oscillatory criteria for Third-Order difference equation with impulses

AbstractIn this paper, we investigate the oscillation of Third-order difference equation with impulses. Some sufficient conditions for the oscillatory behavior of the solutions of Third-order impulsive difference equations are obtained

Bessel Functions in Mass Action. Modeling of Memories and Remembrances

Data from experimental observations of a class of neurological processes (Freeman K-sets) present functional distribution reproducing Bessel function behavior. We model such processes with couples of damped/amplified oscillators which provide time dependent representation of Bessel equation. The root loci of poles and zeros conform to solutions of K-sets. Some light is shed on the problem of filling the gap between the cellular level dynamics and the brain functional activity. Breakdown of time-reversal symmetry is related with the cortex thermodynamic features. This provides a possible mechanism to deduce lifetime of recorded memory.Comment: 16 pages, 9 figures, Physics Letters A, 2015 in pres

Oscillation of third order Impulsive Differential Equations with delay

This paper deals with the oscillation of third order impulsive differential equations with delay. The results of this paper improve and extend some results for the differential equations without impulses. Some examples are givento illustrate the main results

Oscillation of second order self-conjugate differential equation with impulses

AbstractIn this paper, we investigate the oscillation of second-order self-conjugate differential equation with impulses(1)(a(t)(x(t)+p(t)x(t-τ))′)′+q(t)x(t-σ)=0,t≠tk,t⩾t0,(2)x(tk+)=(1+bk)x(tk),k=1,2,…,(3)x′(tk+)=(1+bk)x′(tk),k=1,2,…,where a,p,q are continuous functions in [t0,+∞), q(t)⩾0, a(t)>0, ∫t0∞(1/a(s))ds=∞, τ>0, σ>0, bk>-1, 0<t0<t1 <t2<⋯<tk<⋯ and limk→∞tk=∞. We get some sufficient conditions for the oscillation of solutions of Eqs. (1)–(3)