On the Oscillation of Impulsive Neutral First-order Differential Equations with Variable Arguments

Throughout the article, we study the oscillation of a general class of first-order neutral differential equations in presence of variable delays under the effect of impulses. Due to its importance in applications, there are many papers concerning with the property of oscillation and non-oscillation of neutral delay differential equations. Although, a lot of works are concerning with the oscillation of neutral delay differential equations without impulse or impulsive neutral with constant delays, however few papers dealt with the impulsive neutral and those with variable delays. In this paper, we establish sufficient conditions of certain neutral equations with variable delay arguments. New oscillation criteria are deduced. Our results are based on using equivalence transformation and two useful lemmas to prove the obtained criteria. The results of this paper improve those of [20] by adding several non-linear delay functions to the equations instead of having one delay term. Where it is assumed that the two variable delays satisfying a Lipschitz condition. Moreover we discuss more general non-linear delay functions comparing with those used in [14]. Our results improve and extend some recent results in the literature. An illustrative example is given

Abstract book

Welcome at the International Conference on Differential and Difference Equations & Applications 2015. The main aim of this conference is to promote, encourage, cooperate, and bring together researchers in the fields of differential and difference equations. All areas of differential & difference equations will be represented with special emphasis on applications. It will be mathematically enriching and socially exciting event. List of registered participants consists of 169 persons from 45 countries. The five-day scientific program runs from May 18 (Monday) till May 22, 2015 (Friday). It consists of invited lectures (plenary lectures and invited lectures in sections) and contributed talks in the following areas: Ordinary differential equations, Partial differential equations, Numerical methods and applications, other topics

EQUADIFF 15

Equadiff 15 – Conference on Differential Equations and Their Applications – is an international conference in the world famous series Equadiff running since 70 years ago. This booklet contains conference materials related with the 15th Equadiff conference in the Czech and Slovak series, which was held in Brno in July 2022. It includes also a brief history of the East and West branches of Equadiff, abstracts of the plenary and invited talks, a detailed program of the conference, the list of participants, and portraits of four Czech and Slovak outstanding mathematicians

Nonlinear Acoustic Waves Generated by Surface Disturbances and Their Effect on Lower Thermospheric Composition

Recent nonlinear atmospheric models have provided important insight into acoustic waves generated by seismic events, which may steepen into shocks or saw-tooth trains while also dissipating strongly in the thermosphere. Although they have yielded results that agree with observations of ionospheric perturbations, dynamical models for the diffusive and stratified lower thermosphere often use single gas approximations with height-dependent physical properties (e.g. mean molecular weight, specific heats) that do not vary with time (fixed composition). This approximation is simpler and less computationally expensive than a true multi-fluid model, yet captures the important physical transition between molecular and atomic gases in the lower thermosphere. Models with time-dependent composition and properties have been shown to outperform commonly used models with fixed properties; these time-dependent effects have been included in a one-gas model by adding an advection equation for the molecular weight, finding closer agreement to a true binary-gas model (e.g. Walterscheid and Hickey [2012]). Here, a one-dimensional nonlinear mass fraction approach to multi-constituent gas modeling, motivated by the results of Walterscheid and Hickey, is presented. A flux-differencing finite volume method of is implemented in Clawpack with a Riemann Solver to solve the Euler Equations including multiple species, defined by their mass fractions, as they undergo advection. Viscous dissipation and thermal conduction are applied via a fractional step method. The model is validated with shock tube problems for two species, and then applied to investigate propagating nonlinear acoustic waves from ground to thermosphere, such as following the 2011 Tohoku Earthquake and rocket launches. The limits of applicability are investigated for vertically propagating acoustic waves near the cut-off frequency, and for simulations of steepening waves at finite spatial resolution. The addition of a mass fraction density introduces noticeable fluctuations to the state of the atmosphere that can account for modulation of acoustic waves. The model developed also has potential uses in parametric studies, complementing more costly 2D and 3D models