Results 31 to 40 of about 938 (62)
On an abstract evolution equation with a spectral operator of scalar type
International Journal of Mathematics and Mathematical Sciences, Volume 32, Issue 9, Page 555-563, 2002., 2002 It is shown that the weak solutions of the evolution equation y′(t) = Ay(t), t ∈ [0, T) (0 < T ≤ ∞), where A is a spectral operator of scalar type in a complex Banach space X, defined by Ball (1977), are given by the formula y(t) = e tAf, t ∈ [0, T), with the exponentials understood in the sense of the operational calculus for such operators and the ...
Marat V. Markin
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Semigroup theory applied to options
Journal of Applied Mathematics, Volume 2, Issue 3, Page 131-139, 2002., 2002 Black and Scholes (1973) proved that under certain assumptions about the market place, the value of a European option, as a function of the current value of the underlying asset and time, verifies a Cauchy problem. We give new conditions for the existence and uniqueness of the value of a European option by using semigroup theory.
D. I. Cruz-Báez +1 more
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On nonautonomous second‐order differential equations on Banach space
International Journal of Mathematics and Mathematical Sciences, Volume 26, Issue 1, Page 45-54, 2001., 2001 We show the existence and uniqueness of classical solutions of the nonautonomous second‐order equation: u″(t) = A(t)u′(t) + B(t)u(t) + f(t), 0 ≤ t ≤ T; u(0) = x0, u′(0) = x1 on a Banach space by means of operator matrix method and apply to Volterra integrodifferential equations.
Nguyen Thanh Lan
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Fourth-order Schr\"odinger type operator with singular potentials
, 2016 In this paper we study the biharmonic operator perturbed by an inverse fourth-order potential. In particular, we consider the operator $A=\Delta^2-V=\Delta^2-c|x|^{-4}$ where $c$ is any constant such that ...
Gregorio, Federica, Mildner, Sebastian
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On the operator equation A X − X B = C with unbounded operators A, B, and C
Abstract and Applied Analysis, Volume 6, Issue 6, Page 317-328, 2001., 2001 We find the criteria for the solvability of the operator equation A X − X B = C, where A, B, and C are unbounded operators, and use the result to show existence and regularity of solutions of nonhomogeneous Cauchy problems.
Nguyen Thanh Lan
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Semigroup estimates and fast-slow dynamics in parabolic-hyperbolic systems
Advances in Nonlinear Analysis, 2018 We present a general procedure to describe slow dynamics in parabolic-hyperbolic systems, under suitable assumptions on the terms appearing in the equations. In particular, our strategy relies in semigroup estimates for the evolution system associated to
Strani Marta
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B‐bounded semigroups and implicit evolution equations
Abstract and Applied Analysis, Volume 5, Issue 1, Page 13-32, 2000., 2000 The aim of this paper is to show an application of the recently introduced B‐bounded semigroups in the theory of implicit and degenerate evolution equations. The most interesting feature of this approach is its applicability to problems with noncloseable operators.
J. Banasiak
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Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2016 In this manuscript, we have a tendency to execute Banach contraction fixed point theorem combined with resolvent operator to analyze the exact controllability results for fractional neutral integro-differential systems (FNIDS) with state-dependent delay (
Kailasavalli S. +3 more
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A new characterization of B‐bounded semigroups with application to implicit evolution equations
Abstract and Applied Analysis, Volume 5, Issue 4, Page 227-244, 2000., 2000 We consider the one‐parameter family of linear operators that A. Belleni Morante recently introduced and called B‐bounded semigroups. We first determine all the properties possessed by a couple (A, B) of operators if they generate a B‐bounded semigroup (Y(t))t≥0.
Luisa Arlotti
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Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2019 The manuscript is primarily concerned with the new existence results for fractional neutral integro-differential equation (FNIDE) with nonlocal conditions (NLCs) in Banach spaces.
Mallika D. +3 more
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