Approximation-solvability of nonlinear functional and differential equations

by Wolodymyr V. Petryshyn

Publisher: M. Dekker in New York

Written in English
Cover of: Approximation-solvability of nonlinear functional and differential equations | Wolodymyr V. Petryshyn
Published: Pages: 372 Downloads: 512
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Subjects:

  • Nonlinear functional analysis.,
  • Mappings (Mathematics),
  • Topological degree.

Edition Notes

Includes bibliographical references (p. 339-361) and index.

StatementWolodymyr V. Petryshyn.
SeriesMonographs and textbooks in pure and applied mathematics ;, 171
Classifications
LC ClassificationsQA321.5 .P48 1993
The Physical Object
Paginationxi, 372 p. ;
Number of Pages372
ID Numbers
Open LibraryOL1732004M
ISBN 100824787935
LC Control Number92036577

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The Main Theorem on the Approximation-Solvability of Linear Operator Equations, and the Convergence of the Galerkin Method.- Interpolation Inequalities and a Convergence Trick.- Application to the Refined Banach Fixed-Point Theorem and the Convergence of Iteration Methods.- . In mathematics, a differential equation is an equation that relates one or more functions and their derivatives. The academic year is now displaying on ASSIST. All topics related to differential equations and their applications (ODE's, PDE's, integral equations, functional differential equations, etc. Lyapunov Functionals and Stability of Stochastic Functional Differential Equations by Leonid Shaikhet, , Springer edition, paperback. A system of impulsive degenerate nonlinear parabolic functional- differential inequalities 59 Ludwik Byszewski. Extension of the method of quasilinearization for stochastic initial value problem 69 Farzana A. McRae and N. Shahzad. Existence of asymptotic solutions of second order neutral differential equation with multiple delays.

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This reference/text develops a constructive theory of solvability on linear and nonlinear abstract and differential equations - involving A-proper operator equations in separable Banach spaces, and treats the problem of existence of a solution for equations involving pseudo-A-proper and weakly-A-proper mappings, and illustrates their applications.;Facilitating the understanding of the Cited by: Find many great new & used options and get the best deals for Approximation-Solvability of Nonlinear Functional and Differential Equations by Wolodymyr V.

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New York: Marcel Dekker, © (DLC) (OCoLC) Material Type: Document, Internet resource: Document Type: Internet Resource, Computer File: All Authors / Contributors: Wolodymyr V Petryshyn. A new approach is developed for the solvability of nonlocal problems in Hilbert spaces associated to nonlinear differential equations.

It is based on a joint combination of the degree theory with the approximation solvability method and the bounding functions by: 3. A new approximation solvability method is developed for the study of semilinear differential equations with nonlocal conditions without the compactness of the semigroup and of the nonlinearity.

MILOJEVIĆ, P.S., Approximation solvability results for equations involving nonlinear, perturbations of Fredholm mappings with applications to differential equations, Proc.

Seminar Functional Analysis, Holomorphy and Approximation Theory, M. Dekker, New York, (to appear). Google Scholar. Reseña del editor. This reference/text develops a constructive theory of solvability on linear and nonlinear abstract and differential equations - involving A-proper operator equations in separable Banach spaces, and treats the problem of existence of a solution for equations involving pseudo-A-proper and weakly-A-proper mappings, and illustrates their applications.;Facilitating the Author: Wolodymyr V.

Petryshyn. Milojević, Continuation theory for A-proper and strongly A-closed mappings and their uniform limits and nonlinear perturbations of Fredholm mappings, in Functional Analysis, Holomorphy and Approx.

Theory, Proc. Int. Sem., Rio de Janeiro, AugustNorth Holand Publ. Comp. (Ed. Barroso, to appear). Google Scholar. Integrability of nonlinear differential equations via functional analysis M.

BERGER, P. CHURCH and J. TIMOURIAN Extinction of the solutions of some quasilinear elliptic problems of arbitrary order F. BERNIS On a system of degenerate diffusion equations M.

BERTSCH, M. GURTIN, D. HILHORST and L. PELETIER Based on an external approximation scheme for the underlying Banach space, a nonlinear operator equation is approximated by a sequence of coercive problems. The investigation of controllability problems for nonlinear systems by the methods of fixed-point theory has a long history (see, for example, [2,22] and the references therein).In recent years the corresponding parts of multivalued analysis were applied to obtain various controllability results for systems governed by semilinear differential and functional differential inclusions in infinite.

In this paper, we investigate the nonlinear neutral fractional integral-differential equation involving conformable fractional derivative and integral. First of all, we give the form of the solution by lemma. Furthermore, existence results for the solution and sufficient conditions for uniqueness solution are given by the Leray-Schauder nonlinear alternative and Banach contraction mapping.

J.L. Lions: Problèmes aux limites non homogènes à données irrégulières; une méthode d’approximation.- J.L. Lions: Remarques sur l’approximation régularisée de problèmes aux limites.- W.V. Petryshyn: On the approximation-solvability of nonlinear functional equations in normed linear spaces It is divided into two subvolumes, II/A and II/B, which form a unit.

The present Part II/A is devoted to linear monotone operators. It serves as an elementary introduction to the modern functional analytic treatment of variational problems, integral equations, and partial differential equations of. I want to point out two main guiding questions to keep in mind as you learn your way through this rich field of mathematics.

Question 1: are you mostly interested in ordinary or partial differential equations. Both have some of the same (or very s. Another important application of nonlinear approximation lies in the solu-tion of operator equations.

Most notable, of course, are the adaptive nite element methods for elliptic equations (see Babu ska and Suri ()) as well as the emerging nonlinear wavelet. Nonlinear partial differential equations (PDEs) is a vast area. and practition- ers include applied mathematicians.

analysts. and others in the pure and ap- plied sciences. This introductory text on nonlinear partial differential equations evolved from a graduate course I have taught for many years at the University of Nebraska at Lincoln.

This book highlights real-life applications of differential equations and systems together with the underlying theory and techniques.

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Paperback Approximation Solvability.- Projection Schemes.- A-Proper Mappings.- Approximation Solvability.- Linear A-Proper Maps and Approximation of Isolated Solutions.- Remarks.- Exercises.- § Fourier Analysis and Nonlinear Partial Differential Equations.

This book explains the following topics: First Order Equations, Numerical Methods, Applications of First Order Equations1em, Linear Second Order Equations, Applcations of Linear Second Order Equations, Series Solutions of Linear Second Order Equations, Laplace Transforms, Linear Higher Order Equations, Linear Systems of Differential Equations, Boundary Value Problems and Fourier.

Nonlinear boundary value problems for ordinary differential equations are also considered. Comprised of 14 chapters, this volume first discusses the use of fixed-point theorems in ordered Banach spaces to prove existence and multiplicity result for periodic solutions of semilinear parabolic differential equations of the second order.

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The book discusses new methods for solving stiff systems of ordinary differential equations, stiff elliptic problems encountered in problems of composite material mechanics, Navier-Stokes systems, and nonstationary problems with discontinuous data. On the approximation-solvability of nonlinear functional equations in normed linear spaces.

A two point boundary value problem for a second order differential equation with quadratic growth in the derivative Delbosco, Domenico, Differential and Integral Equations, ; Eigenvalue problem for a class of nonlinear fractional differential equations Han‎, ‎Zhenla, Liu‎, Jian, Sun, Shurong, and Zhao‎, ‎Yige, Annals of Functional Analysis, [13] Li H., Huang F., On the nonlinear eigenvalue problem for perturbations of monotone and accretive operators in Banach spaces, Sichuan Daxue Xuebao,37(3), – [14] Petryshyn W.V., Approximation-Solvability of Nonlinear Functional and Differential Equations, Monogr.

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