共查询到20条相似文献,搜索用时 46 毫秒
1.
Guochun Wen 《中国科学A辑(英文版)》1999,42(7):681-690
The initial-irregular oblique derivative boundary value problems for nonlinear and nondivergence parabolic systems of second
order equations in multiply connected domains are dealt with where coefficients of systems of equations are meaurable. The
uniqueness theorem of solutions for the above problems and somea priori estimates of solutions for the problems are given. And by using the above estimates of solutions and the Leray-Schauder theorem,
the existence of solutions of the initial-boundary value problems is proved. The results are generalizations of corresponding
theorems in literature.
Project supported by the National Natural Science Foundation of China (Grant No. 19671006). 相似文献
2.
高阶微分积分方程的单调迭代法及其应用 总被引:1,自引:0,他引:1
首先利用上下解方法以及微分不等式理论给出了n阶微分积分方程的初值问题解的存在性及其单调迭代法,然后将所得结果应用到n阶微分方程的两点边值问题,得到了n阶非线性两点边值问题解的存在性及其单调迭代法,所得结果推广了已有的结果. 相似文献
3.
《Nonlinear Analysis: Theory, Methods & Applications》2004,56(2):253-272
Crossed symmetric solutions of nonlinear boundary value dynamic problems play an important role in many applications, in particular in adaptive algorithm designs. This article is devoted to the continuation of our investigation on second-order nonlinear companion dynamic boundary value problems on time scales. Monotonically convergent upper and lower solutions of the problems and their quasilinear approximations are investigated. It is shown that, under proper smoothness constraints, the iterative sequences constructed not only converge to the analytic solutions of the desired companion problems monotonically, but also preserve important crossed symmetry properties. The quasilinearization offers an efficient way in the solution approximation. Computational examples are given to illustrate our results. 相似文献
4.
We study a class of even order system boundary value problems with periodic boundary conditions. A series of criteria are obtained for the existence of one, two, any arbitrary number, and even a countably infinite number of positive solutions. Criteria for the nonexistence of positive solutions are also derived. As for the second order case, our results extend, improve, and supplement those in the literature for scalar and system boundary value problems. Several examples are given to demonstrate the applications. Moreover, we obtain conditions for system periodic boundary value problems of a different form to have nontrivial solutions by transforming our main results to such problems. 相似文献
5.
The initial-irregular oblique derivative boundary value problems for linear and nondivergence parabolic complex equations
of second order in multiply connected domains are dealt with, where the coefficients of equations are measurable. Firstly
the uniqueness of solutions for the above problems is introduced, and then somea priori estimates of solutions for the problems are given. By using the above estimates and the Leray-Schauder theorem, the existence
of solutions of the initial-boundary value problems can be proved. The results are generalizations of corresponding theorems
in literature.
Project supported by the National Natural Science Foundation of China (Grant No. 19671006). 相似文献
6.
In this paper, by using the modification function technique and the Leray-Schauder degree method some existence and multiplicity results for sign- changing solutions of certain three-point boundary value problems are obtained. The main result of this paper is an improvement on a former existence result for sign-changing solutions of certain three-point boundary value problems. 相似文献
7.
In this paper, by using the modification function technique and the Leray-Schauder degree method some existence and multiplicity
results for sign- changing solutions of certain three-point boundary value problems are obtained. The main result of this
paper is an improvement on a former existence result for sign-changing solutions of certain three-point boundary value problems. 相似文献
8.
This paper is devoted to studying initial-boundary value problems for semilinear wave equations and derivative semilinear wave equations with variable coefficients on exterior domain with subcritical exponents in n space dimensions. We will establish blow-up results for the initial-boundary value problems. It is proved that there can be no global solutions no matter how small the initial data are, and also we give the life span estimate of solutions for the problems. 相似文献
9.
10.
《Nonlinear Analysis: Theory, Methods & Applications》2005,61(8):1363-1382
In this paper, we develop a theorem for the existence of global solutions of an initial value problems for a class of second-order impulsive integro-differential equations of mixed type in a real Banach space. The results obtained are the generalizations and improvements of various recent results. As an application of the theorem, the existence of global solutions of two mixed boundary value problems for two classes of fourth-order impulsive differential equations are established. 相似文献
11.
12.
In this paper,we investigate the existence of positive solutions of a class higher order boundary value problems on time scales.The class of boundary value problems educes a four-point(or three-point or two-point) boundary value problems,for which some similar results are established.Our approach relies on the Krasnosel’skii fixed point theorem.The result of this paper is new and extends previously known results. 相似文献
13.
S. E. Kholodovskiĭ 《Computational Mathematics and Mathematical Physics》2007,47(9):1489-1495
An efficient method of construction of solutions to a set of boundary value problems with additional interface conditions, more complicated boundary conditions, and so on on the basis of known solutions to classical boundary value problems is proposed. The method is based on the representation of solutions to classical and more complicated problems in the form of expansions into Fourier series with subsequent reduction of one series to the other. As a result, formulas directly expressing solutions to more complicated problems in terms of solutions to classical problems are obtained. On the basis of the well-known solution to the Dirichlet problem on a half plane, solutions to boundary value problems with interface conditions (including generalized conditions of the type of a crack and a screen) on intersecting straight lines for boundary conditions of the first and the third kind are obtained. 相似文献
14.
In this article we present a new fixed point theorem for a class of general mixed monotone operators, which extends the existing corresponding results. Moreover, we establish some pleasant properties of nonlinear eigenvalue problems for mixed monotone operators. Based on them the local existence-uniqueness of positive solutions for nonlinear boundary value problems which include Neumann boundary value problems, three-point boundary value problems and elliptic boundary value problems for Lane-Emden-Fowler equations is proved. The theorems for nonlinear boundary value problems obtained here are very general. 相似文献
15.
Rafal Goebel 《Transactions of the American Mathematical Society》2005,357(6):2187-2203
Value functions for convex optimal control problems on infinite time intervals are studied in the framework of duality. Hamilton-Jacobi characterizations and the conjugacy of primal and dual value functions are of main interest. Close ties between the uniqueness of convex solutions to a Hamilton-Jacobi equation, the uniqueness of such solutions to a dual Hamilton-Jacobi equation, and the conjugacy of primal and dual value functions are displayed. Simultaneous approximation of primal and dual infinite horizon problems with a pair of dual problems on finite horizon, for which the value functions are conjugate, leads to sufficient conditions on the conjugacy of the infinite time horizon value functions. Consequently, uniqueness results for the Hamilton-Jacobi equation are established. Little regularity is assumed on the cost functions in the control problems, correspondingly, the Hamiltonians need not display any strict convexity and may have several saddle points.
16.
On fourth-order elliptic boundary value problems 总被引:4,自引:0,他引:4
C. V. Pao 《Proceedings of the American Mathematical Society》2000,128(4):1023-1030
This paper is concerned with the existence and uniqueness of a solution for a class of fourth-order elliptic boundary value problems. The existence of a solution is proven by the method of upper and lower solutions without any monotone nondecreasing or nonincreasing property of the nonlinear function. Sufficient conditions for the uniqueness of a solution and some techniques for the construction of upper and lower solutions are given. All the existence and uniqueness results are directly applicable to fourth-order two-point boundary value problems.
17.
Tadeusz Jankowski 《Applied mathematics and computation》2010,216(4):1242-1249
We investigate the existence of solutions to nonlinear first-order difference problems with advanced arguments. Sufficient conditions when such problems have solutions (extremal or unique) are given. Linear advanced difference inequalities are also discussed. According to my knowledge, it is a first paper when a monotone iterative method is applied to nonlinear boundary value problems for first-order difference equations with advanced arguments. An example illustrates the theoretical results. 相似文献
18.
D. Willett 《Annali di Matematica Pura ed Applicata》1969,81(1):77-92
Summary The problem of uniqueness of bounded solutions for various nonlinear boundary value problems is considered. Results for problems
with an unbounded interval are obtained. The results obtained for the uniqueness of bounded solutions on the interval (−∞,
∞) are applied to the problem of proving the existence of almost periodic solutions.
Entrata in Redazione il 4 aprile 1968. 相似文献
19.
The solvability of optimal control problems is proved on both weak and strong solutions of a boundary value problem for the nonlinear reaction–diffusion–convection equation with variable coefficients. In the second case, the requirements for smoothness of the multiplicative control are reduced. The study of extremal problems is based on the proof of the solvability of the corresponding boundary value problems and on the qualitative analysis of their solutions properties. The large data existence results for weak solutions, the maximum principle as well as the local existence and uniqueness of a strong solution are established. Moreover, an optimal feedback control problem is considered. Using methods of the theory of topological degree for set-valued perturbations (with aspheric image sets) of generalized monotone operators, we obtain sufficient conditions for the solvability of this problem in the class of weak solutions. 相似文献
20.
The existence of triple solutions for a second-order nonlocal functional boundary value problem is proved by using a fixed-point theorem on cones in Banach spaces due to Leggett and Williams. The obtained results are new even in the ordinary case for three-point boundary value problems discussed quite recently in [Xiaoming He and Weigao Ge (2002). Triple solutions for second-order three-point boundary value problems. J. Math. Anal. Appl., 268, 256–265]. 相似文献