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

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. Theo...

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Published inJournal of inequalities and applications Vol. 2011; no. 1; pp. 1 - 20
Main Author Kamont, Zdzisław
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 22.06.2011
Springer Nature B.V
BioMed Central Ltd
SpringerOpen
Subjects
Analysis
Applications of Mathematics
Classification
Comparison theorems
Derivatives
Differential equations
Functional differential inequalities
Functions (mathematics)
Haar pyramid
Inequalities
Mathematical analysis
Mathematical models
Mathematics
Mathematics and Statistics
Theorems
Weak solutions of initial problems
Haar pyramid
Functional differential inequalities
Comparison theorems
Weak solutions of initial problems
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Abstract 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 .
AbstractList 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.[PUBLICATION ABSTRACT]
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.
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 .
Abstract 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.
ArticleNumber 15
Author Kamont, Zdzisław
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Cites_doi 10.4064/ap88-1-2
10.4064/ap98-1-3
10.1016/0096-3003(94)90048-5
10.1007/BF01776851
10.1016/0362-546X(90)90024-B
10.1016/S0362-546X(01)00907-5
10.1007/BF02411944
10.1216/RMJ-1980-10-1-239
10.1007/978-94-011-4635-7
10.4064/ap-59-1-65-75
ContentType Journal Article
Copyright Kamont; licensee Springer. 2011. This article is published under license to BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License ( ), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Springer International Publishing AG 2011
Copyright_xml – notice: Kamont; licensee Springer. 2011. This article is published under license to BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License ( ), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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Keywords Haar pyramid
Functional differential inequalities
Comparison theorems
Weak solutions of initial problems
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– reference: VanTDTsujiMThai SonNDThe Characteristics method and Its Generalizations for First Order Nonlinear Partial Differential equations2000Boca Raton, FLChapmann and Hall/CRC
– reference: LakshimkanthamVVatsalaASGeneralized Quasilinearization for Nonlinear Problems1995DordrechtKluwer Acadamic Publication
– reference: BainovDKamontZMinchevEOn first order impulsive partial differential inequalitiesAppl Math Comput1994612072300815.35134127430710.1016/0096-3003(94)90048-5
– reference: KamontZKoziełSFunctional differential inequalities with unbounded delayAnn Polon Math20068819371111.35139220495410.4064/ap88-1-2
– reference: KamontZHyperbolic Functional Differential Inequalities1999DordrechtKluwer Acadamic Publishers10.1007/978-94-011-4635-7
– reference: LakshmikanthamVLeelaSDifferential and Integral Inequalities1969New YorkAcadamic Press
– reference: Puźniakowska-GałuchEOn the local Cauchy problem for first order partial differential functional equationsAnn Polon Math20109839611195.35294260748510.4064/ap98-1-3
– reference: TopolskiKOn the uniqueness of viscosity solutions for first order partial differential functional equationsAnn Plon Math19945965750804.351381270302
– reference: SzarskiJDifferential Inequalities1967WarsawPolish Scientific Publishers
– reference: LaddeGSLakshmikanthamVVatsalaAMonotone Iterative Techniques for Nonlinear Differential Equations1985BostonPitmann Advanced Publishing Program
– reference: BrandiPMarcelliCHaar Inequality in hereditary setting and applicationsRend Sem Math Univ Padova1966961771941438297
– reference: SzarskiJComparison theorems for infinite systems of differential functional equations and strongly coupled infinite systems of first order partial differential equationsRocky Mt J Math19801023724657387310.1216/RMJ-1980-10-1-239
– reference: AugustynowiczAKamontZOn Kamke's functions in uniqueness theorems for first order partial differential functional equationsNonlinear Anal TMA1990148378500738.35014105553310.1016/0362-546X(90)90024-B
– reference: Cinquini CibrarioMSopra una class di sistemi de equazioni nonlineari a derivate parziali in piú variabili indipendentiAnn mat pura ed appl19851402232530575.3500780763910.1007/BF01776851
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– reference: KamontZInfinite systems of hyperbolic functional differential inequalitiesNonlinear Anal TMA200251142914451022.35093193093510.1016/S0362-546X(01)00907-5
– reference: ByszewskiLFinite systems of strong nonlinear differential functional degenerate implicit inequalities with first order partial derivativesUniv Iagell Acta Math19922977841172979
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SubjectTerms Analysis
Applications of Mathematics
Classification
Comparison theorems
Derivatives
Differential equations
Functional differential inequalities
Functions (mathematics)
Haar pyramid
Inequalities
Mathematical analysis
Mathematical models
Mathematics
Mathematics and Statistics
Theorems
Weak solutions of initial problems
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Title Weak solutions of functional differential inequalities with first-order partial derivatives
URI https://link.springer.com/article/10.1186/1029-242X-2011-15
https://www.proquest.com/docview/1314384798
https://www.proquest.com/docview/1439768256
http://dx.doi.org/10.1186/1029-242X-2011-15
https://doaj.org/article/ad34fd23dbef43df855922ff1c6d9927
Volume 2011
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