## Differential Equations |

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### Contents

Remarks on the Works of O Perron and L A Lusternik on | 12 |

Perrons Method for Solving the Dirichlet Problem | 20 |

New Proof of the Existence of Solutions for the Dirichlet | 30 |

On the First Boundary Value Problem the Dirichlet Problem | 43 |

On the First Boundary Value Problem for the Heat Equation | 71 |

Studies of the Diffusion with the Increasing Quantity of | 106 |

On the Speed of Propagation of Discontinuities | 133 |

Some Problems in the Theory of Partial Differential Equations | 139 |

On the Uniqueness of a Primitive Function Determined | 299 |

On Reducing the Second Variation to Canonical Form | 312 |

COMMENTARIES | 326 |

On the First Boundary Value Problem for Second Order Parabolic | 352 |

Liindis S A Molchanov | 364 |

On a Problem in the Theory of Elasticity | 400 |

Singular Points of Vector Fields a commentary on article 10 | 420 |

Limit Cycles on the Real and Complex Plane | 464 |

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### Common terms and phrases

Akad algebraic analytic applied Assume assumption behavior belonging boundary point boundary value problem bounded called Cauchy problem close coefficients coincides complex condition consider constant constructed contains continuous convergence coordinates corresponding curve defined definition Denote depends derivatives difference differential equations direction Dirichlet problem domain G elliptic equations equal equivalent established example existence finite function germ given hyperbolic I.G. Petrowsky inequality initial inside integral interval Lemma linear mapping Math Mathematical method Moscow Nauk SSSR neighborhood nonlinear normal O-curves obtained origin parabolic partial differential equations plane polynomial positive possible proof properties proved regular relation remains respect right-hand side satisfies second order shown similar singular point smooth solution space statement studies surface takes theorem theory tions trajectories transformation uniqueness upper vanish variables vector field waves