Existence of positive solutions for fourth-order m-point boundary value problem with variable parameters

In this paper, we investigate the existence of positive solutions for a class of nonlinear fourth-order m-point boundary value problem with two variable parameters. By using the fixed point index theory, we give some new existence results.     

The problem of averaging random structures in terms of distribution functions

A new approach to solving averaging problems for micro-inhomogeneous continua, based on a restatement of the problem in terms of distribution functions, is described. Problems having a variational structure are considered. It is shown that, in terms of distribution functions, they reduce to the problem of minimizing a linear functional, having the meaning of the expectation value of the energy, in a set of distribution functions which is distinguished by an infinite number of linear constants. These constraints express certain matching conditions and contain multipoint distribution functions of the random characteristics of the medium. The constraints form an unlinked chain, the break of which at the n-th step contains only n-point distribution functions. In view of this, a sequence of approximate problems arises.     

Existence of positive solutions to n-point nonhomogeneous boundary value problem

In this paper, we are concerned with the existence of positive solutions to a n-point nonhomogeneous boundary value problem. By using the Krasnoselskii's fixed point theorem in Banach spaces, some sufficient conditions guaranteeing the existence of positive solution is established for the n-point nonhomogeneous boundary value problem.     

Aspects of semiorders within interval orders

Let s_k(n) be the largest integer such that every n-point interval order with no antichain of more than k points includes an s_k(n)-point semiorder. When k = 1, s₁(n) = n since all interval orders with no two-point antichains are chains. Given (c₁,...,c₅) = (1, 2, 3, 4), it is shown that s₂(n) = c_n for n 4, s₃(n) = c_n for n 5, and for all positive n, s₂ (n+4) =s₂(n)+3, s₃(n+5) = s₃(n)+3. Hence s₂ has a repeating pattern of length 4 [1, 2, 3, 3; 4, 5, 6, 6; 7, 8, 9, 9;...], and s₃ has a repeating pattern of length 5 [1, 2, 3, 3, 4; 4, 5, 6, 6, 7; 7, 8, 9, 9, 10;...].

Let s(n) be the largest integer such that every n-point interval order includes an s(n)-point semiorder. It was proved previously that for even n from 4 to 14, and that s(17) = 9. We prove here that s(15) = s(16) = 9, so that s begins 1, 2, 3, 3, 4, 4,..., 8, 8, 9, 9, 9. Since s(n)/n→0, s cannot have a repeating pattern.     

The Initial Boundary Value Problem for Symmetric Long Wave Equations with Nonhomogeneous Boundary Value

Ｔｈｅ　Ｉｎｉｔｉａｌ　Ｂｏｕｎｄａｒｙ　Ｖａｌｕｅ　Ｐｒｏｂｌｅｍ　ｆｏｒ　Ｓｙｍｍｅｔｒｉｃ　Ｌｏｎｇ　Ｗａｖｅ　Ｅｑｕａｔｉｏｎｓ　ｗｉｔｈ　Ｎｏｎｈｏｍｏｇｅｎｅｏｕｓ　Ｂｏｕｎｄａｒｙ　ＶａｌｕｅＭｉａｏＣｈｃｎｘｉａ（苗晨霞）（Ｉｎｓｔｉ...     

Similar constructing method for solving nonhomogeneous mixed boundary value problem of n‐interval composite ode and its application

This paper studies a simple method—Similar Constructing Method (SCM)—for constructing the exact solutions of the nonhomogeneous mixed boundary value problem for sets of n‐interval composite second‐order ordinary differential equation (ODE) with variable coefficient. Then this paper proves the correctness of the solution obtained by SCM. After that, this paper has done simulation experiment. This section uses the SCM to solve the nonhomogeneous boundary value problem of three‐interval composite Bessel equation. Solutions are presented in graphical form for various parameter values, and the influence of parameters on the solution is analyzed. The example shows that using SCM to solve the class of nonhomogeneous mixed boundary value problems of n‐interval composite second‐order linear ODE is easy, convenient, and effective.     

Singular discrete (n, p) boundary value problems

This paper discusses a (n, p) singular discrete boundary value problem. Existence of a nonnegative solution is established.     

Existence of solutions to the nonhomogeneous steady Magnetohydrodynamic equations

We study the nonhomogeneous boundary value problem for the steady Magnetohydrodynamic equations in a two-dimensional bounded domain with multiply connected boundary. We prove that this problem has an admissible solution in an admissible domain if the boundary value is admissible. The proof of the main result uses some property for a weak solution to the transport equations in an admissible domain.     

拟线性系统周期边值问题

The existence and uniqueness results about quasilinear periodic boundary value problems are established by using the global inverse function theorem and the result about the existence and uniquencess of periodic solutions for the periodic boundary value problem of nonhomogeneous linear periodic system.     

Higher order boundary value problems with nonhomogeneous boundary conditions

We study the following nonlinear boundary value problem with nonhomogeneous multi-point boundary condition

     

Initial boundary value problem and asymptotic stabilization of the Camassa-Holm equation on an interval

We investigate the nonhomogeneous initial boundary value problem for the Camassa-Holm equation on an interval. We provide a local in time existence theorem and a weak-strong uniqueness result. Next we establish a result on the global asymptotic stabilization problem by means of a boundary feedback law.     

On solvability of a boundary value problem for a nonhomogeneous biharmonic equation with a boundary operator of a fractional order

This paper is concerned with the solvability of a boundary value problem for a nonhomogeneous biharmonic equation. The boundary data is determined by a differential operator of fractional order in the Riemann-Liouville sense. The considered problem is a generalization of the known Dirichlet and Neumann problems.     

ON SOLVABILITY OF A BOUNDARY VALUE PROBLEM FOR A NONHOMOGENEOUS BIHARMONIC EQUATION WITH A BOUNDARY OPERATOR OF A FRACTIONAL ORDER

This paper is concerned with the solvability of a boundary value problem for a nonhomogeneous biharmonic equation. The boundary data is determined by a differential operator of fractional order in the Riemann-Liouville sense. The considered problem is a generalization of the known Dirichlet and Neumann problems.     

Flows of a polymer fluid in domain with impermeable boundaries

Nonlinear boundary value problems modeling steady polymer flows in domains with impermeable solid walls are studied. The solvability of a nonhomogeneous boundary value problem for the equations governing a polymer flow in the case of an impermeable boundary is proved. The norms of solutions are estimated. The set of weak solutions is shown to be sequentially weakly closed. Additionally, explicit formulas are found for computing the solution of the boundary value problem describing the polymer flow induced by a stretching (shrinking) sheet.     

轴对称渗流中自由边界问题的近似解法

１．问题的提法 本文讨论各向异性非均匀介质的轴对称稳定渗流问题,我们延用［７］的记号。设有一水井（或油井）,其截面如图１所示,ｚ轴为对称轴,Ｄ为渗流区域,其边界为ＡＢＣＥＦＡ,Ｋ＝｛ｋｉｊ（ｒ,ｚ,ｈ,ｑ）｝为对称渗流张量,它依赖于柱坐标中的ｒ,ｚ,压头ｈ＝ｚ＋ｐ／ρｇ及渗流速率其中ｐ为点（ｒ,ｚ）处的压力,ρ为流体密度,ｇ为重力加速度．ｒ０为井的半径,Ｈ１为液面的高度,同时假设当ｒ≥Ｒ时,其渗流速度Ｖ＝０． 由渗流理论,有引入热函数,流函数 Ｄ中一点）,则满足下列一阶非线性方程组其中,若（ｉ＝ １…     

On the nonuniqueness of the solution of a mixed boundary value problem for the Laplace equation

We study the solvability of the mixed boundary value problem for the Laplace equation with three distinct boundary conditions, two of which include two directional derivatives with distinct tilt angles and the remaining one is the first boundary condition. An example of a nontrivial solution of the homogeneous problem is given, and conditions under which the problem has a unique solution are established. The solvability of the problem with a nonhomogeneous first boundary condition is studied.     

非齐次微分方程两点边值问题正解的存在性及多重性

本文考虑一类非齐次微分方程的两点边值问题,得到了一些有关其正解存在性与多重性的精确条件．     

Global strong solutions for 3D viscous incompressible heat conducting Navier‐Stokes flows with the general external force

In this paper, we consider the initial boundary value problem for the nonhomogeneous heat–conducting fluids with non‐negative density and the general external force. We prove that there exists a unique global strong solution to the 3D viscous nonhomogeneous heat–conducting Navier‐Stokes flows if is suitably small.     

一类半无穷区间奇异边值问题正解的存在性

在半无穷区间上讨论带有非齐次边界条件的奇异边值问题正解的存在性,多解性及不存在性．主要结果的证明基于上下解方法,Schauder不动点定理及拓扑度理论．     

Optimal Shape Problems for Eigenvalues

ABSTRACT

We consider the first Dirichlet eigenvalue for nonhomogeneous membranes. For given volume we want to find the domain which minimizes this eigenvalue. The problem is formulated as a variational free boundary problem. The optimal domain is characterized as the support of the first eigenfunction. We prove enough regularity for the eigenfunction to conclude that the optimal domain has finite parameter. Finally an overdetermined boundary value problem on the regular part of the free boundary is given.