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41.
《Mathematische Nachrichten》2018,291(8-9):1240-1268
In this work we deal with solvability of first‐order differential equations in the form , where L is a planar complex vector field, elliptic everywhere except along a simple closed curve Σ on which it is tangent and vanishes of order . In contrast with the local solvability, it is shown that the zero order term p has influence in the solvability in a full neighborhood of Σ. 相似文献
42.
A. Shabanskaya 《代数通讯》2018,46(11):5006-5031
For a sequence of the naturally graded quasi-filiform Leibniz algebra of second type ?2 introduced by Camacho, Gómez, González and Omirov, all possible right and left solvable indecomposable extensions over the field ? are constructed so that the algebra serves as the nilradical of the corresponding solvable Leibniz algebras we find in the paper. 相似文献
43.
G.V. Alekseev 《Applicable analysis》2013,92(2):254-268
We consider control problems for the 2-D Helmholtz equation in an unbounded domain with partially coated boundary. Dirichlet boundary condition is given on one part of the boundary and the impedance boundary condition is imposed on another its part. The role of control in control problem under study is played by boundary impedance. Quadratic tracking–type functionals for the field play the role of cost functionals. Solvability of control problems is proved. The uniqueness and stability of optimal solutions with respect to certain perturbations of both cost functional and incident field are established. 相似文献
44.
O. Jokhadze 《偏微分方程通讯》2013,38(4):367-382
We consider the initial-characteristic problem for nonlinear wave equations with positive power nonlinearity source term. Depending on the power of nonlinearity, we investigate the problem on a global existence and blow-up of solutions of initial-characteristic problem. The question on local solvability of the problem is also considered. 相似文献
45.
46.
《偏微分方程通讯》2013,38(1-2):263-293
Abstract We prove Strichartz type estimates for non-selfadjoint pseudo-differential operators of order m with a curvature condition on the characteristic set. Local solvability results for the corresponding equations with L n/m potential (where n > m stands for the number of variables) and for the corresponding semi-linear equations with a non-linearity of order m/n ≤ α ≤ 2m/(n ? m) follow. This is achieved using a parametrix construction and a Brenner inequality for Fourier integral operators with complex phase. 相似文献
47.
Akbar B. Aliev Anar A. Kazimov Vusala F. Guliyeva 《Mathematical Methods in the Applied Sciences》2013,36(9):1133-1144
In this paper, we investigate the Cauchy problem for a class of the system of semilinear hyperbolic equations with damping. With the use of the Lp → Lq type estimation for the corresponding linear problem and the method of comparison of functional, the existence and nonexistence criteria of global solutions are found. Copyright © 2012 John Wiley & Sons, Ltd. 相似文献
48.
On the Linearized Darboux Equation Arising in Isometric Embedding of the Alexandrov Positive Annulus
Chunhe LI 《数学年刊B辑(英文版)》2013,34(3):435-454
In the present paper, the solvability condition of the linearized Gauss-Codazzi system and the solutions to the homogenous system are given. In the meantime, the solvability of a relevant linearized Darboux equation is given. The equations are arising in a geometric problem which is concerned with the realization of the Alexandrov’s positive annulus in ?3. 相似文献
49.
一类Smarandache方程的可解性问题 总被引:1,自引:0,他引:1
本文研究了包含经典的Euler函数与Smarandache函数的方程.利用初等数论以及分析的方法,给出了此类方程解的一般形式,获得了几个有趣的结果,推广和改进了此类方程的已有结果. 相似文献
50.
Sufficient conditions are found for the global solvability of the weighted Cauchy problem
where f : C([a, b]; R
n) L
loc([a, b]; R
n) is a singular Volterra operator, c
0
R
n, h : [a, b] [0, +] is a function continuous and positive on [a, b], and · is the norm in R
n. 相似文献