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Tuesday, July 28, 2020 | History

5 edition of Some classes of singular equations found in the catalog.

# Some classes of singular equations

## by Siegfried ProМ€ssdorf

Published by North-Holland Pub. Co., sole distributors for the USA and Canada, Elsevier North-Holland in Amsterdam, New York, New York .
Written in English

Subjects:
• Integral equations.

• Edition Notes

Classifications The Physical Object Statement Siegfried Prössdorf ; [translated by Siegfried Dümmel]. Series North-Holland mathematical library ; v. 17 LC Classifications QA431 .P7613 Pagination xiv, 417 p. ; Number of Pages 417 Open Library OL4548447M ISBN 10 0720405017 LC Control Number 77016710

PhD - University of Lyon 1 - France. solutions to some singular differential equations. some existence results for various types of stochastic difference equations including nonlinear ones. The existence of solitary wave, kink wave and periodic wave solutions of a class of singular reaction–diffusion equations is obtained using some effective methods from the dynamical systems theory. Specially, for a class of nonlinear wave equations, fundamental properties of profiles of traveling wave solutions determined by some bounded Cited by:

A singular solution y s (x) of an ordinary differential equation is a solution that is singular or one for which the initial value problem (also called the Cauchy problem by some authors) fails to have a unique solution at some point on the solution. The set on which a solution is singular may be as small as a single point or as large as the full real line. A diﬀerential equation (de) is an equation involving a function and its deriva-tives. Diﬀerential equations are called partial diﬀerential equations (pde) or or-dinary diﬀerential equations (ode) according to whether or not they contain partial derivatives. The order of a diﬀerential equation is the highest order derivative Size: 1MB.

The simplest example of singularities are curves that cross themselves. But there are other types of singularities, like cusps. For example, the equation y 2 − x 3 = 0 defines a curve that has a cusp at the origin x = y = 0. One could define the x-axis as a tangent at this point, but this definition can not be the same as the definition at other points. Sometimes a diﬀerential equation possesses a solution that cannot be ob-tained by assigning values to the parameters in a family of solutions. Such a solution is called a singular solution. Example We will show later on that the nonzero solutions to the diﬀerential equation y0 = ty1 2 are given by y(t) = (t 2 4 +C)2. Find the singular File Size: 1MB.

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### Some classes of singular equations by Siegfried ProМ€ssdorf Download PDF EPUB FB2

: Some Classes of Singular Equations, Vol. 17 (North-Holland Mathematical Library) (): Krupka, Demeter: Books. Search in this book series. Some Classes of Singular Equations.

Edited by Siegfried Prössdorf. Vol Pages ii-v, vii, ix-x, () Download full Some classes of singular equations book. Chapter 9 Singular Equations in Some Countably Normed Spaces and Spaces of Distributions Pages Download PDF.

Featured topics - Analysis on manifolds - Differential forms on jet spaces - Global variational functionals - Euler-Lagrange mapping - Helmholtz form and the inverse problem - Symmetries and the Noether's theory of conservation laws - Regularity and the Hamilton theory - Variational sequences - Differential invariants and natural variational principles - First book on the geometric foundations of Lagrange.

Some classes of singular equations. [Siegfried Prössdorf; Siegfried Dummel] -- This book provides a comprehensive introduction to modern global variational theory on fibred spaces. It is based on differentiation and integration theory of differential forms on smooth manifolds.

Some classes of singular equations. Amsterdam ; New York: North-Holland Pub. ; New York: sole distributors for the USA and Canada, Elsevier North-Holland, (OCoLC) Material Type: Internet resource: Document Type: Book, Internet Resource: All Authors /.

This mono­ graph presents an up to date account of the literature on singular problems. One of our aims also is to present recent theory on singular differential and integral equations to a new and wider audience. The book presents a compact, thorough, and self-contained account for singular by: However, they distinguish between the following types of singular integral equations: (i) those with a semi-infinite or infinite range; (ii) those with a discontinuous derivative in either the kernel or the free term; and (iii) those with either an infinite or nonexisting derivative of some finite order.

In this paper we obtain all solutions which depend only on r for a class of partial differential equations of higher order with singular coefficients. Advertisement. Springer Nature is making SARS-CoV-2 and COVID research free.

Some Solutions for a Class of Singular by: 2. About this book Introduction The final aim of the book is to construct effective discretization methods to solve multidimensional weakly singular integral equations of the second kind on a region of Rn e.g.

equations arising in the radiation transfer theory. One class of singular integral equations of convolution type with Hilbert kernel is studied in the space $$L^{2}[-\pi, \pi]$$ in the article. Such equations can be changed into either a system of discrete equations or a discrete jump problem depending on some parameter via Cited by: The paper is devoted to the study of the solvability of a singular initial value problem for systems of ordinary differential equations.

The main results give sufficient conditions for the existence of solutions in the right-hand neighbourhood of a singular point. In addition, the dimension of the set of initial data generating such solutions is : Josef Diblík, Josef Rebenda, Zdeněk Šmarda.

This course emphasizes concepts and techniques for solving integral equations from an applied mathematics perspective. Material is selected from the following topics: Volterra and Fredholm equations, Fredholm theory, the Hilbert-Schmidt theorem; Wiener-Hopf Method; Wiener-Hopf Method and partial differential equations; the Hilbert Problem and singular integral equations of Cauchy.

Singular Value Decomposition. We saw in that the eigendecomposition can be done only for square matrices. The way to go to decompose other types of matrices that can’t be decomposed with eigendecomposition is to use Singular Value Decomposition (SVD). We will decompose $\bs{A}$ into 3 matrices (instead of two with eigendecomposition).

Advances in Difference Equations will accept high-quality articles containing original research results and survey articles of exceptional merit. Open Thematic Series Submissions to thematic series on this journal are entitled to a 25% discount on the article processing charges unless otherwise stated.

Chapter 5 is focused on the existence, multiplicity, and nonexistence of positive solutions for some classes of systems of nonlinear Riemann–Liouville fractional differential equations with parameters or without parameters, subject to coupled Riemann–Stieltjes integral boundary conditions, and for which the nonlinearities are nonsingular or singular functions.

˜c is the constant vector of the system of equations and A is the matrix of the system's coefficients. We can write the solution to these equations as x 1c r-r =A, () thereby reducing the solution of any algebraic system of linear equations to finding the inverse of the coefficient Size: KB.

These systems are variously called descriptor systems, singular systems, or differential algebraic equations (DAEs). Dynamic Output Feedback Controller Design for a Class of Takagi-Sugeno. Harry Bateman was a famous English mathematician. In writing this book he had endeavoured to supply some elementary material suitable for the needs of students who are studying the subject for the first time, and also some more advanced work which may be useful to men who are interested more in physical mathematics than in the developments of differential geometry and the theory of functions.

A diﬀerential equation, shortly DE, is a relationship between a ﬁnite set of functions and its derivatives. Depending upon the domain of the functions involved we have ordinary diﬀer-ential equations, or shortly ODE, when only one variable appears (as in equations ()-()) or partial diﬀerential equations, shortly PDE, (as in ()).File Size: 1MB.

() Radially symmetric solutions of a class of singular elliptic equations. Proceedings of the Edinburgh Mathematical Society() Some new results for second order boundary value problems. the class handout entitled: Series solutions to a second order linear diﬀerential equation with regular singular points.

The case of an irregular singular point is much more diﬃcult to address, although some techniques do exist for obtaining the solution to a homogeneous second-order linearFile Size: 72KB.When a differential equation is solved, a general solution consisting of a family of curves is obtained.

For Singular solution, in mathematics, solution of a differential equation that cannot be obtained from the general solution gotten by the usual method of solving the differential equation.Stability of a Class of Singular Difference Equations Pham Ky Anh and Dau Son Hoang Department of Mathematics, Vietnam National University, Nguyen Trai, Thanh Xuan, Hanoi, Vietnam Abstract The aim of this paper is to apply Lyapunov functions to obtain some necessary and.