We consider the stochastic differential equation: dXt=(|Xt|)dBt, where B is a Brownian motion and is a non-Hölder Borel function. A sufficient condition of pathwise uniqueness is given. 相似文献
In this paper we give the existence and uniqueness of solutions for boundary value problems of the form u" = f(t, u,u', T1u,T2u), g(u(0),u(1)) = 0, h(w(0), u(1),u'(0), u'(1)) = 0 by means of the upper and lower solution method. 相似文献
In this paper we prove uniqueness of positive solutions to logistic singular problems , , 1$">, 0$"> in , where the main feature is the fact that . More importantly, we provide exact asymptotic estimates describing, in the form of a two-term expansion, the blow-up rate for the solutions near . This expansion involves both the distance function and the mean curvature of .
A uniqueness theorem is proved for trigonometric series and another one is proved for multiple trigonometric series. A corollary of the second theorem asserts that there are two subsets of the -dimensional torus, the first having a countable number of points and the second having points such that whenever a multiple trigonometric series ``converges' to zero at each point of the former set and also converges absolutely at each point of the latter set, then that series must have every coefficient equal to zero. This result remains true if ``converges' is interpreted as any of the usual modes of convergence, for example as ``square converges' or as ``spherically converges.'
We prove a local existence and uniqueness theorem for abstract parabolic problems of the type when the nonlinearity satisfies certain critical conditions. We apply this abstract result to the Navier-Stokes and heat equations.
The Hyogo Ion Beam Medical Center was constructed in 2001 as the world’s first charged particle radiotherapy center where both proton and carbon-ion radiotherapy can be performed. From April 2001 to February 2007, more than 1,400 patients with a variety of cancers were treated. Most of the tumors except for prostate cancer were considered hard to cure with standard treatments such as surgery or conventional x-ray radiotherapy. The clinical results obtained so far are very encouraging, mainly due to the excellent dose localization to the tumor and strong cell killing effects of protons and carbon-ions. The good indications are localized tumors including skull base tumors, head and neck tumors, cancers of the lung, the liver, and the prostate, and bone and soft tissue sarcomas. Charged particle radiotherapy will significantly improve the quality of life of cancer patients and promote their speedy return to normal lives or work if it is used for early stage cancer. 相似文献
We propose a new general definition of Volterra operators. Several types of evolutionary operators, including Volterra ones in the sense of A.N. Tikhonov, satisfy this definition. For equations with generalized Volterra operators we introduce the notions of local, global, and maximally extended solutions. For solutions to nonlinear equations we formulate the existence, uniqueness, and extendability conditions. The theorems proved in this paper imply both known and new results on the solvability of concrete equations. We adduce an example of the application of obtained results to the study of the Cauchy problem for functional differential equations. 相似文献
1. Introduction and Main ResultsIn recent years, singular nonlinear two-point boundary value problems have been studied. For details, see, for instance, [1--14] and references therein. However, the periodicboundary problems with singlllar and discontinuous nonlinearity are quite rarely studied.Motivated by [12,14], we study in this paper a periodic boundary value problem with singularand discontinuous nonlinearity of the form{;<;';<2;::<'> =:<u:>::<,.>,, 5 t 5 27, (1 1)where p is a positi… 相似文献
