Verduyn lunel mathematical institute of the university of leiden, netherlands received 23 july 2007. The main goal of the presented paper is to study a second order functional. Theory of functional differential equations 2nd ed. On the mixed type functionaldifferential equations. We focus specially on the question whether unstable equilibria can be stabilized by appropriately choosing the size of the jump discontinuity. Exponentially dichotomous operators and applications. We study the wellposedness of initial value problems for nonlinear functional differentialalgebraic equations of mixed type. Exponential dichotomies for linear nonautonomous functional. On the other hand the analysis of considered boundary or initial value problem for mixed type functional di erential equations for even order is really complicated. Invariant manifolds and applications for functional.
Neutral mixed type functional di erential equations. Oscillation results for secondorder neutral differential. Hadamard type fractional functional differential equations and inclusions with retarded and advanced arguments. A numerical approach mixedtype functional differential equations.
This book investigates the series of problems concerning linear partial differential equations of the second order in two variables, and possessing the property that the type of the equation changes either on the boundary of or inside the considered. Key worrls and phrnsest mixed functional differential equations, difference differential equations, barbashin type equat,ions, existence and uniqueness of solutions, stability aurl asymptotical stability, initial and boundary value problems, continuous dependence of solutions on initial and boundary functions. Such kind of equations plays a significant role in many branches of. Functional di erential equations with both delayed and advanced arguments are generally referred to as mixed type functional di erential equations mfdes or forwardbackward equations. Such systems can arise from equations which describe traveling waves in a spatial lattice.
Mixed type functional differential equations, lattice differential equations, life cycle model, center manifold, hopf bifurcation, finite dimensional reduction. We also establish the cocycle property and the spectral flow property for such equations, providing an effective means of calculating the fredholm index. Ivanov, on the asymptotic behavior of solutions of a class of first order differential equations with deviating argument of mixed type, asymptotic behavior of functional differential equations, pp. Equations of the mixed type compiles a series of lectures on certain fundamental questions in the theory of equations of mixed type. Properties of thirdorder nonlinear functional differential equations with mixed arguments b. Stability of functional equations in several variables, progress in nonlinear differential equations and their. In this paper, we address the above issues for nonautonomous functional diverential equations of mixed type. The material of chapter 7 is adapted from the textbook nonlinear dynamics and chaos by steven. Smith received july 15, 1999 an example is given to show that the linear autonomous functional differential. Nonoscillation for functional differential equations of mixed type tibor krisztin1 bolyai institute, uni ersity of szeged, aradi ertanuk tere 1, h6720 szeged, hungary email. Liu, iterative method for solutions and coupled quasisolutions of nonlinear integrodifferential equations of mixed type in banach spaces, nonlinear analysis. Functional differential equations with both delayed and advanced arguments are generally referred to as mixed type functional differential equations mfdes or forwardbackward equations.
Existence results for fractional order mixed type functional integrodifferential equations with impulses s. Reducible stochastic functional differential equations. This paper analyzes the solution of linear mixed type functional differential equations with either predetermined or nonpredetermined variables. Functional differential equations of retarded type occur when,, equations. Pdf analytical and numerical investigation of mixedtype. Key worrls and phrnsest mixed functionaldifferential equations, differencedifferential equations, barbashin type equat,ions, existence and uniqueness of solutions, stability aurl asymptotical stability, initial and boundary value problems, continuous dependence of. Positive solutions for nonlinear integrodifferential. This thesis is concerned with a class of linear functional differential equations of mixed. Existence results for fractional order mixed type functional. Discontinuous initial value problems for functional. Pdf on a mixedtype integral equation and fractional. Functiontheoretical methods and functional analysis, in particular the use of a priori estimates, have made it possible to extend significantly the class of equations of mixed type and mixed domains for which existence and uniqueness of a generalized solution can be proved, both for the tricomi problems and for various other mixed problems.
In this paper, we establish the controllability for a class of abstract impulsive mixedtype functional integrodifferential equations with finite delay in a banach space. We are interested in solutions to such problems that admit a single jump discontinuity at time zero. Solutions and stability of generalized mixed type qc. Mixedtype functional differential equations springerlink. We study boundary value differentialdifference equations where the difference terms may contain both advances and delays. The euler lagrange equations that arise from his analysis of the control problem are in fact functional di. Pdf in this paper we study certain systems of mixedtype functional differential equations, from the point of view of the c 0semigroup theory. Jan 16, 2019 in this paper we study some properties of the solutions of a second order system of functional differential equations with maxima, of mixed type, with boundary conditions. On the other hand, if iis singular, we refer to this equation as a functional di erentialalgebraic equation of mixed type mfdae. Systems of functional differential equations with maxima, of.
Computation of mixed type functional differential boundary. Pdf in this note we outline recent developments in the study of mixedtype, or forward backward, functional dieren tial equations. Center manifolds for periodic functional differential. Journal of computational and applied mathematics, 2292, 471479. Differential equations department of mathematics, hkust. On nonlinear partial di erential equations of mixed type guiqiang g.
In particular, it is shown that the relationship between the uniqueness of. Mixed functional differential equations springerlink. Discontinuous initial value problems for funtional. Special attention is paid to connecting orbits, in particular to the modeling of the tails after truncation to a finite interval, and we reformulate these problems as functional differential equations over a bounded domain. Analytical and numerical investigation of mixedtype functional differential equations. The theory of partial differential equations of mixed type with boundary conditions originated in the fundamental research of tricomi 63.
Existence of fractional order mixed type functional integrodifferential equations with nonlocal conditions theorem 2. Center manifold theory for functional differential equations of. Stability and determinacy conditions for mixedtype. A class of functional differential equations of mixed type.
Journal of inequalities and applications hindawi publishing corporation solutions and stability of generalized mixed type qc functional equations in random normed spaces yeol je cho 2 madjid eshaghi gordji 1 somaye zolfaghari 0 vijay gupta 0 department of mathematics, urmia university, urmia, iran 1 department of mathematics, semnan. Another important application area in which equations of the form 1. In this paper we study some properties of the solutions of a second order system of functional differential equations with maxima, of mixed type, with boundary conditions. On nonlinear partial di erential equations of mixed type.
Existence of fractional order mixed type functional. This book discusses various parts of the theory of mixed type partial differential equations with boundary conditions such as. K theory of functional differential equations 2nd ed. In this paper, we study the existence of solutions for a new nonlocal boundary value problem of integrodifferential equations involving mixed left and right caputo and riemannliouville fractional derivatives and riemannliouville fractional integrals of different orders. In this paper we study some properties of the solutions of a second order system of functionaldifferential equations with maxima, of mixed type, with boundary conditions. Lecture notes on mixed type partial differential equations. Murugesu department of mathematics srmv college of arts and science coimbatore641 020, tamil nadu, india. We prove a fredholm alternative theorem for a class of asymptotically hyperbolic linear differential difference equations of mixed type. The existence of monotonic solution for the functional integral equation of the mixed typewill be proved in l10,1. We use perovs fixed point theorem and the weakly picard operator technique. If the inline pdf is not rendering correctly, you can download the pdf file here.
Existence of fractional order mixed type functional integro. Mixedtype differential equation encyclopedia of mathematics. Nonoscillation for functional differential equations of mixed. Solutions and stability of generalized mixed type qca. The study of such equations was motivated by optimal control problems 12 but applications also arise in other. We study the wellposedness of initial value problems for nonlinear functional differential algebraic equations of mixed type. The equations considered in this paper are mixedtype functional equations sometimes known as forwardbackward differential equations that take the form we consider basic existence and. Oscillation results for secondorder neutral differential equations of mixed type. Solutions and stability of generalized mixed type qcafunctional equations in random normed spaces. A numerical approach, journal of computational and applied mathematics on deepdyve, the largest online rental service for scholarly research with thousands of academic publications available at your fingertips. The study of these equations was originally motivated by optimal control. Oscillations of higher order neutral differential equations of mixed type, israel j. Chen oxford centre for nonlinear pde mathematical institute, university of oxford. Pdf nonoscillation for functional differential equations of.
Nonoscillation for functional differential equations of mixed type. In this paper, we establish sufficient conditions for the existence and uniqueness of solutions for boundary value problems of hadamardtype fractional functional differential equations and. This classification depends on whether the rate of change of the current state of the system depends on past values, future values, or both. Hadamardtype fractional functional differential equations and inclusions with retarded and advanced arguments. Pdf mixedtype functional differential equations, holomorphic. A numerical approach ford, neville j lumb, patricia m. Advances and applications linear operators and linear systems, vol 182. Chaplygins classical dynamical equation of mixed type, the theory of regularity of solutions in the sense of tricomi, tricomis fundamental idea and onedimensional. Dhanalakshmi department of mathematics kongunadu arts and science college coimbatore641 029 tamil nadu, india.
Note on the existence of the solutions for functional differential equations of mixed type veronica ana ilea abstract. Mixed type partial differential equations with initial and. Pdf nonoscillation for functional differential equations. The study of these equations was originally motivated by optimal control problems see but applications also arise in other areas. Solutions and stability of generalized mixed type qca functional equations in random normed spaces m. In this paper we present some existence results for the case of a functional di.
The equations considered in this paper are mixedtype functional equations sometimes known as forwardbackward differential equations that take the form u. Many of the examples presented in these notes may be found in this book. Our results rely on the standard tools of functional analysis. Functional differential equations of mixed type mfde are introduced. Dzurina, oscillation of thirdorder nonlinear functional differential equations with mixed arguments, to appear in acta mathematica hungarica. The equations considered in this paper are mixedtype functional equations sometimes known as forwardbackward differential equations that take the form we consider basic existence and uniqueness properties when it1,t2 and we seek solutions u. Conditions characterizing the existence and uniqueness of a solution are given and related to the local stability and determinacy properties of the steady state.
The mixed type partial differential equations are encountered in the theory of transonic flow and they give rise to special boundary value problems, called the tricomi and frankl problems. Nonlinear integrodifferential equations involving mixed. Existence results for fractional order mixed type functional integro differential equations with impulses s. Nonoscillation for functional differential equations of. Differential difference equations are also referred to as retarded, neutral, advanced, and mixed functional differential equations. The qualitative analysis of mixed type functional di erential equations is quite complicated. Properties of thirdorder nonlinear functional differential. Neville ford is dean of research at the university of chester, where he has been employed since 1986. We establish some new existence theorems on the positive solutions for nonlinear integrodifferential equations which do not possess any monotone properties in ordered banach spaces by means of banach contraction mapping principle and cone theory based on some new comparison results. Qualitative properties of solutions for mixed type functional. This paper analyzes the solution of linear mixedtype functional differential equations with either predetermined or nonpredetermined variables.
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