Results 21 to 30 of about 3,995 (269)
Cauchy–Jost function and hierarchy of integrable equations [PDF]
Theoretical and Mathematical Physics, 2015 Properties of the Cauchy--Jost (known also as Cauchy--Baker--Akhiezer) function of the KPII equation are described. By means of the $\bar\partial$-problem for this function it is shown that all equations of the KPII hierarchy are given in a compact and explicit form, including equations on the Cauchy--Jost function itself, time evolutions of the Jost ...
Boiti, M. +2 more
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On Cauchy‐type functional equations
International Journal of Mathematics and Mathematical Sciences, 2004 Let G be a Hausdorff topological locally compact group. Let M(G) denote the Banach algebra of all complex and bounded measures on G. For all integers n ≥ 1 and all μ ∈ M(G), we consider the functional equations , x, y ∈ G, where the functions f, {gi}, {hi}: G → ℂ to be determined are bounded and continuous functions on G.
Elqorachi Elhoucien, Mohamed Akkouchi
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A uniqueness result for the continuity equation in two dimensions [PDF]
, 2014 We characterize the autonomous, divergence-free vector fields $b$ on the plane such that the Cauchy problem for the continuity equation $\partial_t u + div(bu) = 0$ admits a unique bounded solution (in the weak sense) for every bounded initial datum; the
Crippa, Gianluca +8 more
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Stability of Cauchy\u27s equation on Δ+. [PDF]
, 2023 The most famous functional equation f(x+y)=f(x)+f(y) known as Cauchy\u27s equation due to its appearance in the seminal analysis text Cours d\u27Analyse (Cauchy 1821), was used to understand fundamental aspects of the real numbers and the importance of ...
Wells, Holden
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Mathematics, 2023 Cauchy problems are considered for families of, generally speaking, non-Volterra functional differential equations of the second order. For each family considered, in terms of the parameters of this family, necessary and sufficient conditions for the ...
Eugene Bravyi
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Local stability of mappings on multi-normed spaces
Advances in Difference Equations, 2020 First we investigate the Hyers–Ulam stability of the Cauchy functional equation for mappings from bounded (unbounded) intervals into Banach spaces. Then we study the Hyers–Ulam stability of the functional equation f ( x y ) = x g ( y ) + h ( x ) y $f(xy)=
Choonkil Park +4 more
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Electronic Journal of Qualitative Theory of Differential Equations, 2013 Conditions for the unique solvability of the Cauchy problem for a family of scalar functional differential equations are obtained. These conditions are sufficient for the solvability of the Cauchy problem for every equation from the family and are ...
Eugene Bravyi
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On the Tonelli method for the degenerate parabolic Cauchy problem with functional argument [PDF]
Opuscula Mathematica, 2014 The degenerate parabolic Cauchy problem is considered. A functional argument in the equation is of the Hale type. As a limit of piecewise classical solutions we obtain a viscosity solution of the main problem. Presented method is an adaptation of Tonelli'
Krzysztof A. Topolski
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Hyperstability of Cauchy–Jensen functional equations
Indagationes Mathematicae, 2016 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
EL-Fassi, Iz-iddine +2 more
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Stability of the Exponential Functional Equation in Riesz Algebras
Abstract and Applied Analysis, 2014 We deal with the stability of the exponential Cauchy functional equation F(x+y)=F(x)F(y) in the class of functions F:G→L mapping a group (G, +) into a Riesz algebra L. The main aim of this paper is to prove that the exponential Cauchy functional equation
Bogdan Batko
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