Displaying similar documents to “Existence and Uniqueness of Solutions for Partial Differential-Functional Equations of the First Order with Deviating Argument of the Derivative of Unknown Function”

On the Cauchy problem for linear PDEs with retarded arguments at derivatives

Krzysztof A. Topolski (2015)

Annales Polonici Mathematici

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We present an existence theorem for the Cauchy problem related to linear partial differential-functional equations of an arbitrary order. The equations considered include the cases of retarded and deviated arguments at the derivatives of the unknown function. In the proof we use Tonelli's constructive method. We also give uniqueness criteria valid in a wide class of admissible functions. We present a set of examples to illustrate the theory.

On the local Cauchy problem for first order partial differential functional equations

Elżbieta Puźniakowska-Gałuch (2010)

Annales Polonici Mathematici

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A theorem on the existence of weak solutions of the Cauchy problem for first order functional differential equations defined on the Haar pyramid is proved. The initial problem is transformed into a system of functional integral equations for the unknown function and for its partial derivatives with respect to spatial variables. The method of bicharacteristics and integral inequalities are applied. Differential equations with deviated variables and differential integral equations can...

Continuous Dependence of Solutions of Quasidifferential Equations with Non-Fixed Time of Impulses

Plotnikov, V., Kitanov, P. (1998)

Serdica Mathematical Journal

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In this article on quasidifferential equation with non-fixed time of impulses we consider the continuous dependence of the solutions on the initial conditions as well as the mappings defined by these equations. We prove general theorems for quasidifferential equations from which follows corresponding results for differential equations, differential inclusion and equations with Hukuhara derivative.