Comparison theorems for infinite systems of differential-functions equations and strongly coupled infinite systems of first order partial differential equations

Szarski, J.

doi:10.1216/rmj-1980-10-1-239

Cited by 11 publications

(4 citation statements)

References 2 publications

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“…Infinite systems of first order partial functional differential equations were first treated in [18,19]. The existence result presented in [18] is based on a method of successive approximations which was introduced by Ważewski [23] for systems without the functional dependence.…”

Section: T X] and W(τ Y) = W(τ Y) For (τ Y) ∈ D[ϕ(t X)] We Have mentioning

confidence: 99%

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Differentiability with respect to initial functions of solutions to nonlinear hyperbolic functional differential systems

Kamont

2013

Collect. Math.

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A generalized Cauchy problem for nonlinear hyperbolic functional differential systems is considered. A theorem on the existence of weak solutions is proved. The initial problem is transformed into a system of functional integral equations for an unknown function and for their partial derivatives with respect to spatial variables. The existence of solutions of this system is proved by using a method of successive approximations. It is shown a result on the differentiability of solutions with respect to initial functions. This is the main result of the paper.

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Section: T X] and W(τ Y) = W(τ Y) For (τ Y) ∈ D[ϕ(t X)] We Have mentioning

confidence: 99%

“…This method was initiated in [7] for nonlinear systems without functional variables. Differential inequalities and suitable comparison results for infinite systems of hyperbolic functional differential inequalities are given in [13,19].…”

Section: T X] and W(τ Y) = W(τ Y) For (τ Y) ∈ D[ϕ(t X)] We Have mentioning

confidence: 99%

Differentiability with respect to initial functions of solutions to nonlinear hyperbolic functional differential systems

Kamont

2013

Collect. Math.

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“…Hyperbolic functional differential inequalities and suitable comparison results for initial problems are given in [6,7] (Chapter I). Infinite systems of functional differential equations and comparison results are discussed in [8,9]. Impulsive partial differential inequalities were investigated in [10].…”

Section: Introductionmentioning

confidence: 99%

Weak solutions of functional differential inequalities with first-order partial derivatives

Kamont

2011

J Inequal Appl

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The article deals with functional differential inequalities generated by the Cauchy problem for nonlinear first-order partial functional differential equations. The unknown function is the functional variable in equation and inequalities, and the partial derivatives appear in a classical sense. Theorems on weak solutions to functional differential inequalities are presented. Moreover, a comparison theorem gives an estimate for functions of several variables by means of functions of one variable which are solutions of ordinary differential equations or inequalities. It is shown that there are solutions of initial problems defined on the Haar pyramid. Mathematics Subject Classification: 35R10, 35R45.

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“…Results on the existence of solutions are obtained in those papers by using the method of bicharacteristics. Classical solutions in the functional setting were studied in [2], [7], [13], [14]. Cinquini Cibrario solutions of nonlinear differential functional equations were first treated in [3].…”

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confidence: 99%

Generalized Cauchy problems for hyperbolic functional differential systems

Puźniakowska-Gałuch

2014

Ann. Polon. Math.

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A generalized Cauchy problem for hyperbolic functional differential systems is considered. The initial problem is transformed into a system of functional integral equations. The existence of solutions of this system is proved by using the method of successive approximations. Differentiability of solutions with respect to initial functions is proved. It is important that functional differential systems considered in this paper do not satisfy the Volterra condition.

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Comparison theorems for infinite systems of differential-functions equations and strongly coupled infinite systems of first order partial differential equations

Cited by 11 publications

References 2 publications

Differentiability with respect to initial functions of solutions to nonlinear hyperbolic functional differential systems

Differentiability with respect to initial functions of solutions to nonlinear hyperbolic functional differential systems

Weak solutions of functional differential inequalities with first-order partial derivatives

Generalized Cauchy problems for hyperbolic functional differential systems

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