共查询到20条相似文献,搜索用时 15 毫秒
1.
V. V. Marinets 《Journal of Mathematical Sciences》1992,60(3):1449-1455
We investigate a boundary-value problem for systems of nonlinear partial differential equations and construct a modifed two-sided method for approximate integration of this problem. We assume that the right-hand side of the system is a continuous function with bounded first partial derivatives in the given domain.Translated from Vychislitel'naya i Prikladnaya Matematika, No. 59, pp. 24–31, 1986. 相似文献
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CAO Yi LI DongSheng & WANG LiHe College of Science Xi’an Jiaotong University Xi’an China Department of Mathematics The University of Iowa Iowa City IA - USA 《中国科学 数学(英文版)》2011,(3):457-462
For the fully nonlinear uniformly elliptic equation F(D2u) = 0, it is well known that the viscosity solutions are C2,α if the nonlinear operator F is convex (or concave). In this paper, we study the classical solutions for the fully nonlinear elliptic equation where the nonlinear operator F is locally C1,β a.e. for any 0 < β < 1. We will prove that the classical solutions u are C2,α. Moreover, the C2,α norm of u depends on n,F and the continuous modulus of D2u. 相似文献
3.
Ya. Belopolskaya 《Journal of Mathematical Sciences》1998,92(6):4256-4272
A class of nondiagonal systems of nonlinear parabolic equations that can be reduced to a scalar parabolic equation in the
phase space of a larger dimension is described. In view of such a reduction, it is possible to state the maximum principle
for solutions to systems of nonlinear parabolic equations and derive a priori C2+α-estimates for a solution to the Cauchy problem. Bibliography: 19 titles.
Translated fromProblemy Matematicheskogo Analiza, No. 16. 1997, pp. 41–67. 相似文献
4.
Ya. I. Belopol'skaya 《Journal of Mathematical Sciences》1999,97(4):4206-4224
A priori estimates for a solution to a system of fully nonlinear parabolic equations are obtained in a bounded domain under
the condition that the solution vanishes on the boundary of the domain. The method of obtaining a priori estimates is based
on the possibility of reducing the problem under consideration to the Cauchy problem for a scalar equation on a manifold without
boundary in some linear space. Bibliography: 9 titles.
Translated fromProblemy Matematicheskogo Analiza, No. 17, 1997, pp. 46–71. 相似文献
5.
A. V. Ivanov 《Journal of Mathematical Sciences》1978,10(2):217-240
We consider classes of elliptic equations of the form (x,u,u
D
2
u)=0 for the solutions of which one establishes local and global a priori estimates for D
2
u=. In particular, one investigates the Monge-Ampere equation, and for its convex solutions one constructs a local and a global estimate for D
2
u and a local estimate for.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 59, pp. 31–59, 1976. 相似文献
6.
G. Gaprindashvili 《Georgian Mathematical Journal》1995,2(1):21-36
The periodic boundary value problem for systems of secondorder ordinary nonlinear differential equations is considered. Sufficient conditions for the existence and uniqueness of a solution are established. 相似文献
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8.
The first initial-boundary-value problem for a uniformly parabolic and uniformly nondegenerate operator is considered. An
a priori estimate for an admissible solution is established. In view of the generalized Hessian, it is possible to avoid the
growth conditions which are usual in the theory of uniformly elliptic and uniformly parabolic operators. Bibliography: 19
titles.
Translated fromProblemy Matematicheskogo Analiza, No. 16. 1997, pp. 112–133. 相似文献
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Xiangshan Kong Haitao Li Shulan Qin Hongxin Zhao 《Journal of Applied Mathematics and Computing》2017,54(1-2):81-93
This paper studies the bifurcation of positive solutions for a three-point boundary-value problem of nonlinear fractional differential equations with parameter. Using the topological degree theory and the bifurcation technique, the existence of positive solutions is investigated and some sufficient conditions are obtained. The study of two illustrative examples shows that the obtained new results are effective. 相似文献
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13.
Zheng Songmu 《数学学报(英文版)》1987,3(3):237-246
This paper is concerned with the global existence of the second initial boundary value problem for fully nonlinear parabolic
equations. It is proved that when the initial data is sufficiently small, the problem admits a unique global solution. Moreover,
ast goes to +∞, the solution exponentially decays to zero. 相似文献
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We prove a uniqueness theorem in terms of value distribution for meromorphic solutions of a class of nonlinear partial differential equations of first order, which shows that such solutions f are uniquely determined by the zeros and poles of f−cj (counting multiplicities) for two distinct complex numbers c1 and c2. 相似文献
17.
K. Hosseini R. Ansari P. Gholamin 《Journal of Mathematical Analysis and Applications》2012,387(2):807-814
In recent years, many approaches have been utilized for finding the exact solutions of nonlinear systems of partial differential equations. In this paper, the first integral method introduced by Feng is adopted for solving some important nonlinear systems of partial differential equations, including, KdV, Kaup–Boussinesq and Wu–Zhang systems, analytically. By means of this method, some exact solutions for these systems of equations are formally obtained. The results obtained confirm that the proposed method is an efficient technique for analytic treatment of a wide variety of nonlinear systems of partial differential equations. 相似文献
18.
The starting point of this work is a paper by Alvarez, Lasry and Lions (1997) concerning the convexity and the partial convexity of solutions of fully nonlinear degenerate elliptic equations. We extend their results in two directions. First, we deal with possibly sublinear (but epi-pointed) solutions instead of 1-coercive ones; secondly, the partial convexity of C2 solutions is extended to the class of continuous viscosity solutions. A third contribution of this paper concerns C1,1 estimates for convex viscosity solutions of strictly elliptic nonlinear equations. To finish with, all the tools and techniques introduced here permit us to give a new proof of the Alexandroff estimate obtained by Trudinger (1988) and Caffarelli (1989). 相似文献
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Xiaohong Li 《Journal of Mathematical Analysis and Applications》2011,378(2):723-733
The aim of the paper is to derive a priori estimates and obtain the Harnack-type inequalities of positive weak solutions for the nonlinear differential inequalities in an exterior domain or interior domain. By using the test function method developed by Mitidieri and Pohozaev, we extend and improve some known results proved by Serrin and Zou, Bidaut-Véron and Pohozaev. 相似文献