Sufficient conditions of consensus (synchronization) in networks described by digraphs and consisting of identical deterministic SIMO systems are derived. Identical and nonidentical control gains (positive arc weights) are considered. Connection between admissible digraphs and nonsmooth hypersurfaces (sufficient gain boundary) is established. Necessary and sufficient conditions for static consensus by output feedback in networks consisting of certain class of double integrators are rediscovered. Scalability for circle digraph in terms of gain magnitudes is studied. Examples and results of numerical simulations are presented.

Ibragim A. Junussov

Static Consensus in Passifiable Linear Networks

The numerical algorithm for solving &#x201c;first-order linear differential equation in fuzzy environment&#x201d; is discussed. A scheme, namely, &#x201c;Runge-Kutta-Fehlberg method,&#x201d; is described in detail for solving the said differential equation. The numerical solutions are compared with (i)-gH and (ii)-gH differential (exact solutions concepts) system. The method is also followed by complete error analysis. The method is illustrated by solving an example and an application.

Sankar Prasad Mondal

Susmita Roy

Biswajit Das

Numerical Solution of First-Order Linear Differential Equations in Fuzzy Environment by Runge-Kutta-Fehlberg Method and Its Application

Sabbavarapu Nageswara Rao

Multiplicity of Positive Solutions for Fractional Differential Equation with <svg  xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"   style="vertical-align:-3.42943pt" height="10.2124pt" version="1.1" viewBox="-0.0498162 -6.78297 7.83752 10.2124" width="7.83752pt"><g transform="matrix(.013,0,0,-0.013,0,0)"><path id="g113-113" d="M570 304C570 398 525 448 414 448C385 448 343 445 312 434L329 511L321 518C297 504 262 482 244 460L233 411C195 397 159 381 128 358L135 332C160 347 189 360 224 373L111 -147C97 -210 84 -218 17 -231L13 -257L254 -247L259 -218L233 -216C183 -212 177 -202 189 -142L218 -1C238 -10 266 -12 283 -12C351 3 429 48 483 105C543 168 570 242 570 304ZM482 289C482 161 380 33 304 33C278 33 248 51 233 69L303 396C326 400 352 403 369 403C428 403 482 380 482 289Z" /></g></svg>-Laplacian Boundary Value Problems

For the thin-film model of a viscous flow which originates from lubrication approximation and has a full nonlinear curvature term, we prove existence of nonnegative weak solutions. Depending on initial data, we show algebraic or exponential dissipation of an energy functional which implies dissipation of the solution arc length that is a well known property for a Hele-Shaw flow. For the classical thin-film model with linearized curvature term, under some restrictions on parameter and gradient values, we also prove analytically the arc length dissipation property for positive solutions. We compare the numerical solutions for both models, with nonlinear and with linearized curvature terms. In regimes when solutions develop finite time singularities, we explain the difference in qualitative behaviour of solutions.

Matthew Michal

Marina Chugunova

Roman Taranets

Qualitative Behaviour of Solutions in Two Models of Thin Liquid Films

We establish some important results about improper fuzzy Riemann integrals; we prove some properties of fuzzy Laplace transforms, which we apply for solving some fuzzy linear partial differential equations of first order, under generalized Hukuhara differentiability.

ElHassan ElJaoui

Said Melliani

On Fuzzy Improper Integral and Its Application for Fuzzy Partial Differential Equations

We consider an intrahost malaria model allowing for antigenic variation within a single species. The host&#x2019;s immune response is compartmentalised into reactions to major and minor epitopes. We investigate the dynamics of the model, paying particular attention to bifurcation and stability of the uniform nonzero endemic equilibrium. We establish conditions for the existence of an equivariant Hopf bifurcation in a ring of antigenic variants, characterised by time delay.

Israel Ncube

Equivariant Hopf Bifurcation in a Time-Delayed Ring of Antigenic Variants

A new result of solvability for a wide class of systems of variational equations depending on parameters and governed by nonmonotone operators is found in a Banach real and reflexive space with applications to Dirichlet and Neumann problems related to nonlinear elliptic systems.

Luisa Toscano

Speranza Toscano

A New Result Concerning the Solvability of a Class of General Systems of Variational Equations with Nonmonotone Operators: Applications to Dirichlet and Neumann Nonlinear Problems

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<p><em>International Journal of Differential Equations</em> publishes research on differential equations, and related integral equations, from all scientists who use differential equations as tools within their own discipline.</p>


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International Journal of Differential Equations publishes research on differential equations, and related integral equations, from all scientists who use differential equations as tools within their own discipline.

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International Journal of Differential Equations

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International Journal of Differential Equations