四阶非线性常微分方程非线性两点边值问题解的存在唯一性

本文利用Ｂｏｌｚａｎｏ定理，给出了四阶非线性常微微分方程具有非线性边界条件的两点边值问题（１）（２）２，（１）（２）３存在解与存在唯一解的一般性结果，并将所得结果应用于Ｌｉｐｓｃｈｉｚ方程，对Ｌｉｐｓｃｈｉｔｚ方程满足边界条件（２）２，（２）３的边值问题给出了存在解与存在唯一解的具体的充分条件。     

On a result of Ozawa concerning uniqueness of meromorphic functions

In this paper we prove a uniqueness theorem for meromorphic functions sharing three values with some weight which improves some known results.     

A Strong Maximum Principle for parabolic equations with the p-Laplacian

We prove the Strong Maximum Principle (SMP) under suitable assumptions for a class of quasilinear parabolic problems with the p  -Laplacian, p>1$p>1$, on bounded cylindrical domains of R^N+1${\mathbb{R}}^{N+1}$,

_∂tu−_Δpu−λ|u|^p−2u≥0,${\partial }_{t}u-{\mathrm{\Delta }}_{p}u-\lambda {|u|}^{p-2}u\ge 0,$

with nonnegative initial–boundary conditions and λ≤0$\lambda \le 0$, and we give some counterexamples to the SMP if some of our assumptions are violated. We show that the Hopf Maximum Principle holds for 1<p<2$1<p<2$, and give a counterexample to it for p>2$p>2$. Also the Weak Maximum Principle for λ≤_λ1$\lambda \le {\lambda }_1$ is established.     

“A priori” estimates, uniqueness and existence of positive solutions of Yamabe type equations on complete manifolds

We study the asymptotic behaviour of non-negative solutions of Yamabe type equations on a complete Riemannian manifold. Then we provide a comparison result, based on a form of the weak maximum principle at infinity, which together with the “a priori” estimates previously obtained, yields uniqueness under very general Ricci assumptions. The paper ends with an existence result and an application to the non-compact Yamabe problem.     

On Best Approximations from RS-sets in Complex Banach Spaces

The concept of an RS-set in a complex Banach space is introduced and the problem of best approximation from an RS-set in a complex space is investigated. Results consisting of characterizations, uniqueness and strong uniqueness are established,     

On complexity of unconstrained hyperbolic 0-1 programming problems

Single- and multiple-ratio unconstrained hyperbolic 0-1 programming problems are considered. We prove that checking whether these problems have a unique solution is NP-hard. Furthermore, we show that finding the global maximizer of problems with unique solution remains NP-hard. We also discuss complexity of local search and approximability for multiple-ratio problems.     

Weighted sharing three values and Brosch's theorem

This paper studies the idea of weighted sharing and proves two main theorems which generalize some results given by G. Brosch, Q. Zhang and other authors.     

Riesz operators and the complete norm topology

We show that a non-injective Riesz operator on an infinite-dimensional Banach space X does not determine the complete norm topology of X. We also show that an injective operator with trivial generalized range determines the complete norm topology of X. Finally this result is used to settle the crucial role of the non-injectivity condition in our first result.     

Some uniqueness results for a class of quasilinear elliptic eigenvalue problems

Existence and uniqueness results are obtained for positive radial solutions of a class of quasilinear elliptic equations in aN-ball or an annulus without monotone assumptions on the nonlinear termf. It is also proved that there is no non-radial positive solution. Supported by the Youth Foundations of National Education Commuttee and the Committee on Science and Technology of Henan Province