THE EXISTENCE AND LOCAL UNIQUENESS OF MULTI-PEAK SOLUTIONS TO A CLASS OF KIRCHHOFF TYPE EQUATIONS

In this paper,we study the existence and local uniqueness of multi-peak solutions to the Kirchhoff type equations-(ε^(2)a+εb∫_(R^(3))|■u|^(2))△u+V(x)u=u^(p),u>0 in R^(3),which concentrate at non-degenerate critical points of the potential function V(x),where a,b>0,1<p<5 are constants,andε>0 is a parameter.Applying the Lyapunov-Schmidt reduction method and a local Pohozaev type identity,we establish the existence and local uniqueness results of multi-peak solutions,which concentrate at{a_(i)}1≤i≤k,where{a_(i)}1≤i≤k are non-degenerate critical points of V(x)asε→0.

ON UNIQUENESS OF MEROMORPHIC FUNCTIONS WITH SHARED-SETS IN AN ANGULAR DOMAIN

In this article, we deal with the uniqueness problems on meromorphic functions sharing two finite sets in an angular domain instead of the whole plane C. In particular, we investigate the uniqueness for meromorphic functions of infinite order in an angular domain and obtain some results. Moreover, examples show that the conditions in theorems are necessary.

The Uniqueness of Meromorphic Functions with Common Range Sets and Deficient Values

In this paper, the uniqueness of meromorphic functions with common range sets and deficient values are studied. This result is related to a question of Gross.

On the uniqueness of entire functions

We study the uniqueness of entire functions and prove the following theorem: Let f(z) and g(z) be two nonconstant entire functions; n and k two positive integers with n>2k+4. If the zeros of both f(z) and g(z) are of multiplicity at least n, and f (k)(z) and g (k)(z) share 1 CM, then either f(z)=c 1e cz, g(z)= c 2e -cz, where c 1, c 2 and c are three constants satisfying (-1) kc 1c 2c 2k= 1, or f(z)≡g(z).

On Uniqueness Problem of Meromorphic Functions Sharing Values with Their q-shifts

In this paper, the uniqueness problems on meromorphic function f(z) of zero order sharing values with their q-shift f(qz + c) are studied. It is shown that if f(z) and f(qz + c) share one values CM and IM respectively, or share four values partially, then they are identical under an appropriate deficiency assumption.

Generalization of Uniqueness Theorems for Entire and Meromorphic Functions

In this paper, we deal with the uniqueness problems on entire and meromorphic functions con- cerning differential polynomials that share fixed-points. Moreover, we generalise and improve some results of Weichuan Lin, Hongxun Yi, Meng Chao, C. Y. Fang, M. L. Fang and Junfeng xu.

Some Uniqueness Results of Q-Shift Difference Polynomials Involving Sharing Functions

In this paper, we mainly study the uniqueness of specific q-shift difference polynomials and of meromorphic functions, which share a common small function and get the corresponding results. In addition, we also investigate the problem of value distribution on q-shift difference polynomials of entire functions.

THE UNIQUENESS FOR ALGEBROID FUNCTIONS OF FINITE ORDER

In this article,we discuss,by Nevanlinna theory,the influence of multiple values and deficiencies on the uniqueness problem of algebroid functions.We get several uniqueness theorems of algebroid functions which include an at most 3v-valued theorem.These results extend the existing achievements of some scholars.

Generalization of Uniqueness of Meromorphic Functions Sharing Fixed Point

In this paper, we study the uniqueness problems of entire and meromorphic functions concerning differential polynomials sharing fixed point and obtain some results which generalize the results due to Subhas S. Bhoosnurmath and Veena L. Pujari [1].

On Uniqueness of Meromorphic Functions That Share Two Values

A problem of meromorphic functions that share two values is discussed, and two results recently obtained respectively by Yi H. X. and Song G. D. & Li N. are improved.

Existence and Uniqueness of Positive Periodic Solutions for First-order Functional Differential Equations

In this paper, we prove the existence and uniqueness of positive periodic solutions for first-order functional differential equation y＇（t） = α（t）y（t） ＋ f（t, y（t -τ-（t））） ＋ g（t）by using two fixed point theorems of general α-concave operators and homogeneous operators in ordered Banach spaces.

Existence and Uniqueness of Positive (Almost) Periodic Solutions for a Neutral Multi-Species Logarithmic Population Model with Multiple Delays and Impulses

In this paper, by using the contraction mapping principle and constructing a suitable Lyapunov functional, we established a set of easily applicable criteria for the existence, uniqueness and global attractivity of positive periodic solution and positive almost periodic solution of a neutral multi-species Logarithmic population model with multiple delays and impulses. The results improve and generalize the known ones in [1], as an application, we also give an example to illustrate the feasibility of our main results.

Uniqueness Theorems of Meromorphic Functions That Share Four Values

For the open question 'If two nonconstant meromorphic functions share three values IM and share a fourth value CM, then do the functions necessarily share all four values CM?', the author studies the case when four values are shared IM and their counting functions satisfy an additional condition. The author obtains some results which answer this question partially.

The uniqueness of meromorphic functions concerning small functions

We prove that the Nevanlinna five-point-theorem on the uniqueness of meromorphic func-tions is valid for five small meromorphic functions.

UNIQUENESS OF ENTIRE FUNCTIONS SHARING ONE VALUE

We deal with the problem of entire functions sharing one value weakly. Moreover, we improve and generalize some former results obtained by J.-F.Chen, et al. [6], Y.Xu and H.L.Qiu [4], M.L. Fang [5], C.C. Yang, and X.H. Hua [3].

Uniqueness Theorems for Meromorphic Functions of Order Less than One

In this paper we study the uniqueness of certain meromorphic functions. It is shown that any two nonconstant meromorphic functions of order less than one, that share four values IM or six values SCM, must be identical. As a consequence, a result due to W. W. Adams and E. G. Straus is generalized.

The Uniqueness of the Entire Functions Whose n-th Powers Share a Small Function with Their Derivatives

In this paper, we prove the following result： Let f（z） be a transcendental entire function, Q（z） ≡ 0 be a small function of f（z）, and n ≥ 2 be a positive integer. If fn（z） and（fn（z）） share Q（z） CM, then f（z） = ce 1 nz, where c is a nonzero constant. This result extends Lv＇s result from the case of polynomial to small entire function.

UNIQUENESS OF MEROMORPHIC FUNCTIONS WHOSE NONLINEAR DIFFERENTIAL POLYNOMIALS SHARE ONE VALUE OR HAVE THE SAME FIXED POINTS IN AN ANGULAR DOMAIN

In this article, we study the uniqueness question of nonconstant meromorphic functions whose nonlinear differential polynomials share 1 or have the same fixed points in an angular domain. The results in this article improve Theorem 1 of Yang and Hua [26], and improve Theorem 1 of Fang and Qiu [6].

Uniqueness Problems for Meromorphic Functions that Share Three Values

This paper investigate the uniqueness problems for meromorphic functions that share three values CM and proves a uniqueness theorem on this topic which can be used to improve some previous related results.

Uniqueness Theorem of Algebroidal Functions in the Unit Disc

In this paper, the uniqueness of algebroidal functions in the unit disc is investigated. Suppose that W（z） and M（z） are v-valued and k-valued algebroidal functions in the unit disc, respectively. Let e^iθ be a b-cluster point of order co or order ρ（x） of the algebroidal function W（z） or M（z）. It is shown that if -↑E（aj, W（z）） = -↑E（aj,M（z）） holds in the domain {｜z｜ 〈 1}∩Ω（θ-δ,θ＋δ）, where b, aj （j = 1,…, 2v ＋ 2k ＋ 1） are complex constants, then W（z） = M（z）. The same results are obtained for the case that e^iθ is a Borel point of order co or order ρ（x） of the algebroidal function W（z） or M（z）.