Results 81 to 90 of about 3,995 (269)
Stability of generalized additive Cauchy equations
International Journal of Mathematics and Mathematical Sciences, 2000 A familiar functional equation f(ax+b)=cf(x) will be solved in the class of functions f:ℝ→ℝ. Applying this result we will investigate the Hyers-Ulam-Rassias stability problem of the generalized additive Cauchy equation f(a1x1+⋯+amxm+x0)=∑i=1mbif(ai1x1 ...
Soon-Mo Jung, Ki-Suk Lee
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Front Propagation Through a Perforated Wall
Communications on Pure and Applied Mathematics, EarlyView.ABSTRACT We consider a bistable reaction– diffusion equation ut=Δu+f(u)$u_t=\Delta u +f(u)$ on RN${\mathbb {R}}^N$ in the presence of an obstacle K$K$, which is a wall of infinite span with many holes. More precisely, K$K$ is a closed subset of RN${\mathbb {R}}^N$ with smooth boundary such that its projection onto the x1$x_1$‐axis is bounded and that ...
Henri Berestycki +2 more
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Energy Science &Engineering, EarlyView.Mine‐water immersion tests reveal pronounced coal weakening (vs. minor concrete degradation), identifying coal pillars as the stability‐limiting component in composite dams. A coupled FEINN framework quantifies extreme‐pressure stability and ranks multi‐parameter designs via a normalized multi‐indicator scheme, enabling optimized dam configuration for ...
He Wen +6 more
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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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Cauchy's functional equation in the mean
Advances in Mathematics, 1984 The following theorem is proved. If \(\alpha \geq 1\) and \(f\in L^{\alpha}(0,z)\) for every \(z>0\) and if \[ \lim_{z\to \infty}(z^{- 2}\int^{z}_{0}\int^{z}_{0}| f(x+y)-f(x)- f(y)|^{\alpha}dxdy)=0, \] then there exists an A such that \(\lim_{z\to \infty}(z^{-1}\int^{z}_{0}| f(x)- Ax|^{\alpha}dx)=0.\) Similar theorems and connections to \textit{D.
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The structure of Cauchy function of a vector quasidifferential equation
Matematychni Studii, 2004 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Makhneĭ, O. V., Tatsiĭ, R. M.
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On the Hyers-Ulam-Rassias Stability of the Cauchy Linear Functional Equation
, 2015 [[abstract]]In this paper, we obtain the general solution and we provide a proof of the functional stability in the spirit of Hyers-Ulam, Th. M. Rassias and P. Gˇavruta for the Cauchy linear functional equation f(x + y + a) = f(x) + f(y), where f : E1 −!
Belaid, Bouikhalene +1 more
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Functional Differential Equations
, 2018 The goal of this chapter is to apply the theories developed in the previous chapters to functional differential equations. In Section 7.1 retarded functional differential equations are rewritten as abstract Cauchy problems and the integrated semigroup ...
Pierre Magal +3 more
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Cauchy’s functional equation and extensions: Goldie’s equation and inequality, the Gołąb–Schinzel equation and Beurling’s equation [PDF]
, 2015 The Cauchy functional equation is not only the most important single functional equation, it is also central to regular variation. Classical Karamata regular variation involves a functional equation and inequality due to Goldie; we study this, and its ...
N. H. Bingham +3 more
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Mathematical Methods in the Applied Sciences, Volume 48, Issue 6, Page 6425-6446, April 2025.ABSTRACT The well‐posedness results for mild solutions to the fractional neutral stochastic differential system with Rosenblatt process with Hurst index Ĥ∈12,1$$ \hat{H}\in \left(\frac{1}{2},1\right) $$ is discussed in this article. To demonstrate the results, the concept of bounded integral contractors is combined with the stochastic result and ...
Dimplekumar N. Chalishajar +3 more
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