共查询到20条相似文献,搜索用时 15 毫秒
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We provide sufficient conditions for the existence and uniqueness of solutions to a stochastic differential equation which arises in the price impact model developed by Bank and Kramkov (2011) and . These conditions are stated as smoothness and boundedness requirements on utility functions or Malliavin differentiability of payoffs and endowments. 相似文献
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We consider the initial–boundary value problem of a damped wave equation with singular nonlinearity, which describes an electrostatic micro-electro-mechanical system (MEMS) device. The results of the pull-in voltage λ? being the critical threshold for global existence and quenching are obtained: if the applied voltage λ<λ?, then the equation admits a unique global small solution that exponentially converges to the minimal steady state, while large solution may quench in finite time; if λ>λ?, then any solution quenches in finite time. Finally, in the sense of the viscosity dominated limit, the asymptotic relation of solutions between the hyperbolic equation and the parabolic one is investigated. Also the related error estimates in arbitrary order are derived. 相似文献
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Wolfgang Sander 《manuscripta mathematica》1986,54(4):439-452
We derive the representation of generalized additive measures of information, depending on two probability distributions and having the sum property with a regular generating function. This family of measures includes the Shannon entropy, the entropy of degree (,), the generalized information energy, the sine entropy and the generalized directed divergence. 相似文献
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Hans Ringstrm 《纯数学与应用数学通讯》2004,57(5):657-703
We consider a class of space‐times for which the essential part of Einstein's equations can be written as a wave map equation. The domain is not the standard one, but the target is hyperbolic space. One ends up with a 1 + 1 nonlinear wave equation, where the space variable belongs to the circle and the time variable belongs to the positive real numbers. The main objective of this paper is to analyze the asymptotics of solutions to these equations as t → ∞. For each point in time, the solution defines a loop in hyperbolic space, and the first result is that the length of this loop tends to 0 as t?1/2 as t → ∞. In other words, the solution in some sense becomes spatially homogeneous. However, the asymptotic behavior need not be similar to that of spatially homogeneous solutions to the equations. The orbits of such solutions are either a point or a geodesic in the hyperbolic plane. In the nonhomogeneous case, one gets the following asymptotic behavior in the upper half‐plane (after applying an isometry of hyperbolic space if necessary):
- 1 The solution converges to a point.
- 2 The solution converges to the origin on the boundary along a straight line (which need not be perpendicular to the boundary).
- 3 The solution goes to infinity along a curve y = const.
- 4 The solution oscillates around a circle inside the upper half‐plane.
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Stevo Stevi? 《Journal of Mathematical Analysis and Applications》2011,376(1):317-5318
The boundedness character of positive solutions of the following max-type difference equation
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《Applied Mathematics Letters》2006,19(8):699-705
We discuss the dispersal of a chemical, emitted from a point source, into a reacting medium. The diffusion and reaction are such that a front emerges, so that at all times the chemical remains confined to a bounded domain around the source. We focus on the final stationary state which is a non-standard Stefan-type boundary value problem for an Emden–Fowler equation. We prove its existence and uniqueness and obtain, analytically as well as numerically, bounds for the location of the front and for the concentration profile. 相似文献
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This note shows that every positive solution to the following third order non–autonomous max-type difference equationwhen is a three-periodic sequence of positive numbers, is periodic with period three. The same result was proved for the following min-type difference equation 相似文献
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Fred M. Hoppe 《Aequationes Mathematicae》1980,20(1):33-37
It is shown that a 1-1 correspondence exists between the possible Yaglom conditional limits when a subcritical Galton-Watson process is initiated with an arbitrary probability distribution and the invariant measures of the process. This is proven by an examination of the relevant Schröder and Abel functional equations. 相似文献
15.
Let p
*
=n/(n−2) and n≥3. In this paper, we first classify all non-constant solutions of
We then establish a sup + inf and a Moser-Trudinger type inequalities for the equation −Δu=u
+
p*
. Our results illustrate that this equation is much closer to the Liouville problem −Δu=e
u
in dimension two than the usual critical exponent equation, namely is.
Received: 11 March 2002; in final form: 8 July 2002 /
Published online: 16 May 2003 相似文献
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Donato Triginate 《Journal of Difference Equations and Applications》2013,19(5-6):111-129
Cyclic reduction is a powerful technique in numerical linear algebra for solving tridiagonal systems. It can be classified in the class of divide and conquer methods. Some of its surprising properties have been studied recently essentially in the case of diagonally dominant matrices. In this paper the case of Toeplitz matrices will be considered. A complete analysis of the properties of the cyclic reduction will be done by studing an associate system of nonlinear difference equations. 相似文献
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G. Papaschinopoulos C.J. Schinas 《Journal of Mathematical Analysis and Applications》2007,326(1):155-164
In this paper we investigate the boundedness, the persistence and the attractivity of the positive solutions of the nonautonomous difference equation
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Seick Kim 《Journal of Mathematical Analysis and Applications》2009,351(1):326-333
We study a certain one-dimensional, degenerate parabolic partial differential equation with a boundary condition which arises in pricing of Asian options. Due to degeneracy of the partial differential operator and the non-smooth boundary condition, regularity of the generalized solution of such a problem remained unclear. We prove that the generalized solution of the problem is indeed a classical solution. 相似文献