奇异椭圆边值问题正解的不存在定理

根据非线性理论 ,利用上、下解方法 ,给出了一类奇异椭圆型方程边值问题正解的不存在性结果。证明了方程 -Δu =- f ( u) +λh( x)在有界区域Ω R″上的 0边值问题 ,当非线性项达到一定程度 ,即 f( s)≥ ms-γ, s∈ ( 0 ,+∞ ) ,γ≥ 1时 ,问题无正解。

一类中立型非线性差分方程的正解不存在定理

本文根据一个正序列{y_n}满足差分不等式 y_(n+1)≤Q_ny_n-F_n所得的结论,对一类中立型非线性差分方程推导了正解不存在定理。

带脉冲的时滞双曲型系统正解的不存在性定理及其应用

建立了具有脉冲的时滞双曲型系统正解的不存在性定理 。

关于调和映照的两个不存在性定理

研究以复射影空间CPn 和四元数射影空间QPn 为始流形或靶流形的调和映照的稳定性 ,得到了两个不存在性定理 .

一类带位势非线性热方程解的不存在性定理

研究与向量场有关的非线性次椭圆热方程.通过选取合适的测试函数,应用反证法证明了与之相关的初边值问题解的不存在性定理,将欧式空间及Heisenberg群上的结果推广至满足Hrmander有限秩条件的光滑向量场.

关于调和映照的一个不存在性定理

本文在得到广义Grassmann流形具有常数数量曲率的结果的基础上，利用一个矩阵不等式证明了到广义Grassmann流形的调和映照的一个不存在性定理，并推广了吴光磊等人的结果．

Existence of Multiple Positive Solutions for Higher-Order p-Laplacian Boundary Value Problems

The existence of multiple positive solutions for a class of higher order p Laplacian boundary value problem is studied. By means of the Leggett Williams fixed point theorem in cones, existence criteria which ensure the existence of at least three positive solutions of the boundary value problem are established.

Positive Solutions of a Semilinear Elliptic Equation with Coefficient That Changes Sign

We prove the existence of a positive solution to the problem-Δu=a(x)f(u), x∈Ω, u(x)=0,x∈Ω,where Ω is a bounded domain in R n with smooth boundary, a(x) is allowed to change sign.

An Existence Theorem of Positive Solution for Fourth-order Superlinear Semipositone Eigenvalue Problems

In this paper we investigate the existence of positive solution for a class of fourth_order superlinear semipositone eigenvalue problems. This class of problems usually describes the deformation of the elastic beam whose both end_points are fixed.

3-调和映照稳定性的几个结果

本文求出了3-调和映照的第二变分公式,得出了关于平凡和非平凡稳定的3-调和映照的几个存在和不存在性定理。

Singular Perturbations of Boundary Value Problems for a Class of Quasilinear Differential Equations

In this paper, the Nagumo theorem and the fixed-point theorem are used to prove the existence and the uniqueness and to estimate the asymptotic expansion of the shock solutions of the boundary value problems for a class of quasilinear differential equations, the asymptotic expansion of solution of any orders including boundary is obtained.

Existence Theorems for a Fifth-Order Boundary Value Problem

Abstract： In this paper, we study the existence of a solution for fifth-order boundary value problem{u（5）（t）＋f（t,u（t）,u＂（t）=0,0〈t〈1）/u（0）=u＇（0）=u＇（1）=u＂（1）=u（4）（0）=0 Where f ∈ C（[0,1] × R2, R）. By placing certain restrictions on the nonlinear term f, we prove the existence of at least one solution to the boundary value problem with the use of the lower and upper solution method and Schauder fixed-point theorem. The construction of lower or upper solution is also present.ed. Boundary value problems of very similar type are also considered.

Existence of Positive Solutions for a Third-Order Three-Point Boundary Value Problem with Semipositone Nonlinearity *

The existence of positive solutions is investigated for following semipositone nonlinear third-order three-point BVP ω''(t) - λf(t,w(t)) = 0, 0 ≤ t ≤ 1, ω(0) = ω'(n) = ω'(1) = 0.

The hyper-surfaces with two linear dependent mean curvature functions in space forms

We formulate a class of functionals in space forms such that its critical points include the r-minimal hyper-surface and the minimal hyper-surface as special cases. We obtain the algebraic, differential and variational characteristics of the critical surfaces determined by the critical points. We prove the Simons' type nonexistence theorem which indicates that in the unit sphere, there exists no stable critical surfaces, and the Alexandrov's type existence theorem which indicates that in Euclidean space, the sphere is the only stable critical surfaces.

Closed Geodesics and Volume Growth of Open Manifolds with Sectional Curvature Bounded from Below

In this paper, the relationship between the existence of closed geodesics and the volume growth of complete noncompact Riemannian manifolds is studied. First the authors prove a diffeomorphic result of such an n-m2nifold with nonnegative sectional curvature, which improves Marenich-Toponogov＇s theorem. As an application, a rigidity theorem is obtained for nonnegatively curved open manifold which contains a clesed geodesic. Next the authors prove a theorem about the nonexistence of closed geodesics for Riemannian manifolds with sectional curvature bounded from below by a negative constant.

Homoclinic solutions in periodic difference equations with saturable nonlinearity

In this paper, a periodic difference equation with saturable nonlinearity is considered. Using the linking theorem in combination with periodic approximations, we establish sufficient conditions on the nonexistence and on the existence of homoclinic solutions. Our results not only solve an open problem proposed by Pankov, but also greatly improve some existing ones even for some special cases.

SOLVABILITY OF VECTOR KY FAN INEQUALITIES WITH APPLICATIONS

This paper aims to study the solvability of vector Ky Fan inequalities and the compactness of its solution sets.For vector-valued functions with the cone semicontinuity and the cone quasiconvexity in infinite dimensional spaces,the authors prove some existence results of the solutions and the compactness of the solution sets.Especially,some results for the vector Ky Fan inequalities on noncompact sets are built and the compactness of its solution sets are also discussed.As applications,some existence theorems of the solutions of vector variational inequalities are obtained.

On a Quasilinear Elliptic Equation with Superlinear Nonlinearities

This work is devoted to studying a quasilinear elliptic boundary value problem with superlinear nonlinearities in a weighted Sobolev space in a domain of R^N. Based on the Galerkin method, Brouwer's theorem and the weighted compact Sobolev-type embedding theorem, a new result about the existence of solutions is revealed to the problem.

L_p-DICHOTOMY OF LINEAR DIFFERENTIAL EQUATIONS IN AN ARBITRARY BANACH SPACE

The notion of Lp-dichotomy for linear differential equations with possibly unbounded oper-ator is introduced. By help of Banach fixed point theorem sufficient conditions for the existenceof bounded solutions of nonlinear differential equations with an Lp-dichotomous linear part areobtained.