# Differential Equations

DOI link for Differential Equations

Differential Equations book

# Differential Equations

DOI link for Differential Equations

Differential Equations book

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Part II of the Selected Works of Ivan Georgievich Petrowsky, contains his major papers on second order Partial differential equations, systems of ordinary. Differential equations, the theory, of Probability, the theory of functions, and the calculus of variations. Many of the articles contained in this book have Profoundly, influenced the development of modern mathematics. Of exceptional value is the article on the equation of diffusion with growing quantity of the substance. This work has found extensive application in biology, genetics, economics and other branches of natural science. Also of great importance is Petrowsky's work on a Problem which still remains unsolved - that of the number of limit cycles for ordinary differential equations with rational right-hand sides.

## TABLE OF CONTENTS

part |181 pages

Petrowsky’s Articles on Partial Differential Equations

chapter 1|8 pages

#### Remarks on the Works of O. Perron and L.A. Lusternik on the Dirichlet Problem *

chapter 2|10 pages

#### Perron’s Method for Solving the Dirichlet Problem *

chapter 3|13 pages

#### New Proof of the Existence of Solutions for the Dirichlet Problem by the Finite Difference Method *

chapter 4|28 pages

#### On the First Boundary Value Problem (the Dirichlet Problem) for Elliptic Equations and Some Properties of Functions Satisfying These Equations *

chapter 5|35 pages

#### On the First Boundary Value Problem for the Heat Equation *

chapter 6|27 pages

#### Studies of the Diffusion with the Increasing Quantity of the Substance; Its Application to a Biological Problem *

chapter 7|6 pages

#### On the Speed of Propagation of Discontinuities of Displacement Derivatives on the Surface of a Non-Homogeneous Elastic Body of Arbitrary Shape *

chapter 8|33 pages

#### Some Problems in the Theory of Partial Differential Equations *

chapter 9|20 pages

#### Contribution of S.N. Bernstein to the Theory of Partial Differential Equations *

part |85 pages

Petrowsky’s Articles on Ordinary Differential Equations

chapter 10|61 pages

#### On the Behavior of Integral Curves for a System of Ordinary Differential Equations in a Neighborhood of a Singular Point *

chapter 11|21 pages

#### On the Number of Limit Cycles for the Equation d y d x = P ( x , y ) Q ( x , y ) , where P and Q are Polynomials of Degree 2 * [ 1 ]

part |49 pages

Petrowsky’s Articles on the theory of Probability and other Problems of Analysis