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101.
Franziska Kühn 《Mathematische Nachrichten》2019,292(2):358-376
We present an existence result for Lévy‐type processes which requires only weak regularity assumptions on the symbol with respect to the space variable x. Applications range from existence and uniqueness results for Lévy‐driven SDEs with Hölder continuous coefficients to existence results for stable‐like processes and Lévy‐type processes with symbols of variable order. Moreover, we obtain heat kernel estimates for a class of Lévy and Lévy‐type processes. The paper includes an extensive list of Lévy(‐type) processes satisfying the assumptions of our results. 相似文献
102.
103.
Basak Karpuz 《Mathematical Methods in the Applied Sciences》2019,42(9):2993-3001
In this paper, we give new sufficient conditions for both oscillation and nonoscillation of the delay dynamic equation where and satisfy τ(t) ≤ σ(t) for all large t and . As an important corollary, we obtain the time scale invariant integral condition for nonoscillation: for all large t. Also, with some examples, we show that newly presented results are sharp. 相似文献
104.
Julia Calatayud Juan Carlos Corts Marc Jornet 《Mathematical Methods in the Applied Sciences》2019,42(18):7259-7267
In this paper, we address the problem of approximating the probability density function of the following random logistic differential equation: P′(t,ω)=A(t,ω)(1?P(t,ω))P(t,ω), t∈[t0,T], P(t0,ω)=P0(ω), where ω is any outcome in the sample space Ω. In the recent contribution [Cortés, JC, et al. Commun Nonlinear Sci Numer Simulat 2019; 72: 121–138], the authors imposed conditions on the diffusion coefficient A(t) and on the initial condition P0 to approximate the density function f1(p,t) of P(t): A(t) is expressed as a Karhunen–Loève expansion with absolutely continuous random coefficients that have certain growth and are independent of the absolutely continuous random variable P0, and the density of P0, , is Lipschitz on (0,1). In this article, we tackle the problem in a different manner, by using probability tools that allow the hypotheses to be less restrictive. We only suppose that A(t) is expanded on L2([t0,T]×Ω), so that we include other expansions such as random power series. We only require absolute continuity for P0, so that A(t) may be discrete or singular, due to a modified version of the random variable transformation technique. For , only almost everywhere continuity and boundedness on (0,1) are needed. We construct an approximating sequence of density functions in terms of expectations that tends to f1(p,t) pointwise. Numerical examples illustrate our theoretical results. 相似文献
105.
The inverse problem of determining 2D spatial part of integral member kernel in integro‐differential wave equation is considered. It is supposed that the unknown function is a trigonometric polynomial with respect to the spatial variable y with coefficients continuous with respect to the variable x. Herein, the direct problem is represented by the initial‐boundary value problem for the half‐space x>0 with the zero initial Cauchy data and Neumann boundary condition as Dirac delta function concentrated on the boundary of the domain . Local existence and uniqueness theorem for the solution to the inverse problem is obtained. 相似文献
106.
107.
108.
Areeba Ikram 《Journal of Difference Equations and Applications》2019,25(6):757-775
ABSTRACTWe will establish uniqueness of solutions to boundary value problems involving the nabla Caputo fractional difference under two-point boundary conditions and give an explicit expression for the Green's functions for these problems. Using the Green's functions for specific cases of these boundary value problems, we will then develop Lyapunov inequalities for certain nabla Caputo BVPs. 相似文献
109.
110.
A new exactly solvable ()-dimensional complex nonlinear wave equation exhibiting rich analytic properties has been introduced. A rogue wave (RW), localized in space–time like Peregrine RW solution, though richer due to the presence of free parameters is discovered. This freedom allows to regulate amplitude and width of the RW as needed. The proposed equation allows also an intriguing topology changing accelerated dark soliton solution in spite of constant coefficients in the equation. 相似文献