Oscillation of forced impulsive differential equations with pp-Laplacian and nonlinearities given by Riemann-Stieltjes integrals

In this article, we study the oscillation of second order forced impulsive differential equation with $p$-Laplacian and nonlinearities given by Riemann-Stieltjes integrals of the form \begin{equation*} \left( p(t)\phi _{\gamma }\left( x^{\prime }(t)\right) \right) ^{\prime}+q_{0}\left( t\right) \phi _{\gamma }\left( x(t)\right)+\int_{0}^{b}q\left( t,s\right) \phi _{\alpha \left( s\right) }\left(x(t)\right) d\zeta \left(s\right) =e(t), t\neq \tau _{k}, \end{equation*} with impulsive conditions \begin{equation*} x\left( \tau _{k}^{+}\right) =\lambda _{k}~x\left( t_{k}\right), x^{\prime }\left( \tau _{k}^{+}\right) =\eta _{k}~x^{\prime }\left( \tau_{k}\right), \end{equation*} where \phi _{\gamma }\left( u\right) :=\left\vert u\right\vert ^{\gamma } \mbox{{\rm sgn}\,}u, $\gamma, b\in \left( 0,\infty \right),$ $\alpha \in C\left[ 0,b\right)$ is strictly increasing such that $0\leq \alpha \left( 0\right) <\gamma <\alpha \left( b-\right)$, and $\left\{ \tau_{k}\right\}_{k\in {\mathbb{N}}}$ is the the impulsive moments sequence. Using the Riccati transformation technique, we obtain sufficient conditions for this equation to be oscillatory

Asymptotic solutions of forced nonlinear second order differential equations and their extensions

Using a modified version of Schauder's fixed point theorem, measures of non-compactness and classical techniques, we provide new general results on the asymptotic behavior and the non-oscillation of second order scalar nonlinear differential equations on a half-axis. In addition, we extend the methods and present new similar results for integral equations and Volterra-Stieltjes integral equations, a framework whose benefits include the unification of second order difference and differential equations. In so doing, we enlarge the class of nonlinearities and in some cases remove the distinction between superlinear, sublinear, and linear differential equations that is normally found in the literature. An update of papers, past and present, in the theory of Volterra-Stieltjes integral equations is also presented

Asymptotic behavior of third order functional dynamic equations with γ\gamma-Laplacian and nonlinearities given by Riemann-Stieltjes integrals

In this paper, we study the third-order functional dynamic equations with $\gamma$-Laplacian and nonlinearities given by Riemann-Stieltjes integrals \begin{equation*} \left\{ r_{2}\left( t\right) \phi _{\gamma _{2}}\left( \left[ r_{1}\left( t\right) \phi _{\gamma _{1}}\left( x^{\Delta }\left( t\right) \right) \right] ^{\Delta }\right) \right\} ^{\Delta }+\int_{a}^{b}q\left( t,s\right) \phi _{\alpha \left( s\right) }\left( x(g\left( t,s\right) )\right) d\zeta \left( s\right) =0, \end{equation*} on an above-unbounded time scale $\mathbb{T}$, where $\phi_{\gamma }(u):=\left\vert u\right\vert^{\gamma -1}u$ and $\int_{a}^{b}f\left( s\right) d\zeta \left( s\right)$ denotes the Riemann-Stieltjes integral of the function $f$ on $[a,b]$ with respect to $\zeta$. Results are obtained for the asymptotic and oscillatory behavior of the solutions. This work extends and improves some known results in the literature on third order nonlinear dynamic equations

Oscillation of a time fractional partial differential equation

We consider a time fractional partial differential equation subject to the Neumann boundary condition. Several sufficient conditions are established for oscillation of solutions of such equation by using the integral averaging method and a generalized Riccati technique. The main results are illustrated by examples

Differential/Difference Equations

The study of oscillatory phenomena is an important part of the theory of differential equations. Oscillations naturally occur in virtually every area of applied science including, e.g., mechanics, electrical, radio engineering, and vibrotechnics. This Special Issue includes 19 high-quality papers with original research results in theoretical research, and recent progress in the study of applied problems in science and technology. This Special Issue brought together mathematicians with physicists, engineers, as well as other scientists. Topics covered in this issue: Oscillation theory; Differential/difference equations; Partial differential equations; Dynamical systems; Fractional calculus; Delays; Mathematical modeling and oscillations

Fractional Differential Equations, Inclusions and Inequalities with Applications

During the last decade, there has been an increased interest in fractional differential equations, inclusions, and inequalities, as they play a fundamental role in the modeling of numerous phenomena, in particular, in physics, biomathematics, blood flow phenomena, ecology, environmental issues, viscoelasticity, aerodynamics, electrodynamics of complex medium, electrical circuits, electron-analytical chemistry, control theory, etc. This book presents collective works published in the recent Special Issue (SI) entitled "Fractional Differential Equation, Inclusions and Inequalities with Applications" of the journal Mathematics. This Special Issue presents recent developments in the theory of fractional differential equations and inequalities. Topics include but are not limited to the existence and uniqueness results for boundary value problems for different types of fractional differential equations, a variety of fractional inequalities, impulsive fractional differential equations, and applications in sciences and engineering