Results 61 to 70 of about 4,267,250 (176)
Cauchy Problem for a Darboux Integrable Wave Map System and Equations of Lie Type
Symmetry, Integrability and Geometry: Methods and Applications, 2013 The Cauchy problem for harmonic maps from Minkowski space with its standard flat metric to a certain non-constant curvature Lorentzian 2-metric is studied.
Peter J. Vassiliou
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Abstract and Applied Analysis, 2013 Let be a real normed space with dimension greater than 2 and let be a real functional defined on . Applying some ideas from the studies made on the conditional Cauchy functional equation on the restricted domain of the vectors of equal norm and the ...
Margherita Fochi, Gabriella Viola
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On a generalization of the Cauchy functional equation
Aequationes Mathematicae, 1992 The paper deals with the functional equation \(g(ax+by) =Ag(x)+Bg(y) +L(x,y)\) where \(g\) maps a nonempty subset \(P\) of a vector space \(X\), satisfying the condition \(aP+bP \subset P\), into a vector space \(Y\), and \(L:X \times X \to Y\) is a given biadditive mapping.
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Continuity equations and ODE flows with non-smooth velocity [PDF]
, 2014 In this paper we review many aspects of the well-posedness theory for the Cauchy problem for the continuity and transport equations and for the ordinary differential equation (ODE). In this framework, we deal with velocity fields that are not smooth, but
Crippa, Gianluca, Ambrosio, Luigi
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Application of the functional calculus to solving of infinite dimensional heat equation
Karpatsʹkì Matematičnì Publìkacìï, 2016 In this paper we study infinite dimensional heat equation associated with the Gross Laplacian. Using the functional calculus method, we obtain the solution of appropriate Cauchy problem in the space of polynomial ultradifferentiable functions.
S.V. Sharyn
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On a general Hyers-Ulam stability result
International Journal of Mathematics and Mathematical Sciences, 1995 In this paper, we prove two general theorems about Hyers-Ulam stability of functional equations. As particular cases we obtain many of the results published in the last ten years on the stability of the Cauchy and quadratic equation.
Costanz Borelli, Gian Luigi Forti
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Cauchy problems and invariant measures for one stochastic functional-differential equation
Науковий вісник Ужгородського університету. Серія: Математика і інформатика, 2019 We deal with Cauchy problem for one stochastic functional-differential equation. We study the existence, uniqueness and continuous dependence on initial function of so-called mild solution to this problem.
A. N. Stanzhytskyi, A. O. Tsukanova
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Isomorphisms and Derivations in Lie C*-Algebras
Abstract and Applied Analysis, 2007 We investigate isomorphisms between C*-algebras, Lie C*-algebras, and JC*-algebras, and derivations on C*-algebras, Lie C*-algebras, and JC*-algebras associated with the Cauchy–Jensen functional equation 2f((x+y/2)+z)=f(x)+f(y)+2f(z).
Choonkil Park, Jong Su An, Jianlian Cui
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Fixed Points and Stability of the Cauchy Functional Equation in C∗-Algebras
Fixed Point Theory and Applications, 2009 Using the fixed point method, we prove the generalized Hyers-Ulam stability of homomorphisms in C∗-algebras and Lie C∗-algebras and of derivations on C∗-algebras and Lie C∗-algebras for the Cauchy functional equation.
Choonkil Park
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On an alternative functional equation related to the Cauchy equation
Aequationes Mathematicae, 1982 We consider the following problem: Let (G, +) be an abelian group,B a complex Banach space,a, b∈B,b≠0,M a positive integer; find all functionsf:G →B such that for every (x, y) ∈G ×G the Cauchy differencef(x+y)−f(x)−f(y) belongs to the set {a, a+b, a+2b, ...,a+Mb}.
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