10,513 research outputs found

    Functional Inequalities: New Perspectives and New Applications

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    This book is not meant to be another compendium of select inequalities, nor does it claim to contain the latest or the slickest ways of proving them. This project is rather an attempt at describing how most functional inequalities are not merely the byproduct of ingenious guess work by a few wizards among us, but are often manifestations of certain natural mathematical structures and physical phenomena. Our main goal here is to show how this point of view leads to "systematic" approaches for not just proving the most basic functional inequalities, but also for understanding and improving them, and for devising new ones - sometimes at will, and often on demand.Comment: 17 pages; contact Nassif Ghoussoub (nassif @ math.ubc.ca) for a pre-publication pdf cop

    Oscillation Criteria for Fourth Order Nonlinear Positive Delay Differential Equations with a Middle Term

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    In this article, we establish some new criteria for the oscillation of fourth order nonlinear delay differential equations of the form (Equation presented) provided that the second order equation (Equation presented) is nonoscillatiory or oscillatory. This equation with g(t) = t is considered in [8] and some oscillation criteria for this equation via certain energy functions are established. Here, we continue the study on the oscillatory behavior of this equation via some inequalities

    New oscillation results to fourth order delay differential equations with damping

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    This paper is concerned with the oscillation of the linear fourth order delay differential equation with damping \begin{equation*} \left(r_3(t)\left(r_2(t)\left(r_1(t)y'(t)\right)'\right)'\right)'+p(t)y'(t)+q(t)y(\tau(t))=0 \end{equation*} under the assumption that the auxiliary third order differential equation \begin{equation*} \left(r_3(t)\left(r_2(t)z'(t)\right)'\right)'+\frac{p(t)}{r_1(t)}z(t)=0 \end{equation*} is nonoscillatory. In addition, a couple of examples is provided to illustrate the relevance of the main results

    Oscillation of certain fourth order functional differential equations

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    Some new criteria for the oscillation of fourth-order nonlinear functional differential equations of the special form are established.Встановлено деякі нові критерії коливання нелінійних функціональних диференціальних рівнянь спеціального вигляду

    Differential/Difference Equations

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    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

    Oscillation Results for Even Order Trinomial Functional Differential Equations with Damping

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    In this paper, we investigate the oscillatory behavior of solutions to a certain class of nonlinear functional differential equations of the even order with damping. By using the integral averaging technique and Riccati type transformations, we prove four new theorems on the subject. Several examples are also considered to illustrate the main results
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