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.

The Existence of Solutions for Kirchhoff-Type Equations with General Singular Terms

We study the existence of solutions for Kirchhoff-type equations.Firstly,we use the Sobolev inequality and the weakly lower semi-continuity of the norm to prove that the corresponding function can reach the global minimum.Then,we use the variational method and some analytical techniques to obtain the existence of the positive solution of the equation whenλis small enough.

THE EXISTENCE AND LOCAL UNIQUENESS OF MULTI-PEAK POSITIVE SOLUTIONS TO A CLASS OF KIRCHHOFF EQUATION

In the present paper,we consider the nonlocal Kirchhoff problem-(ε^2a+εb∫|■u|^2)Δu+u=Q(x)u^p,u>0 in R^3,,where a,b>0,1<p<5 andε>0 is a parameter.Under some assumptions on Q(x),we show the existence and local uniqueness of positive multi-peak solutions by LyapunovSchmidt reduction method and the local Pohozaev identity method,respectly.

A NOTE ON THE UNIQUENESS AND THE NON-DEGENERACY OF POSITIVE RADIAL SOLUTIONS FOR SEMILINEAR ELLIPTIC PROBLEMS AND ITS APPLICATION

In this paper, we are concerned with the uniqueness and the non-degeneracy of positive radial solutions for a class of semilinear elliptic equations. Using detailed ODE anal- ysis, we extend previous results to cases where nonlinear terms may have sublinear growth. As an application, we obtain the uniqueness and the non-degeneracy of ground states for modified SchrSdinger equations.

Existence of Monotone Positive Solution for a Fourth-Order Three-Point BVP with Sign-Changing Green’s Function

This paper is concerned with the following fourth-order three-point boundary value problem , where , we discuss the existence of positive solutions to the above problem by applying to the fixed point theory in cones and iterative technique.

Existence and Uniqueness of Weak Solutions to the p-biharmonic Parabolic Equation

We consider an initial-boundary value problem for a p-biharmonic parabolic equation. Under some assumptions on the initial value, we construct approximate solutions by the discrete-time method. By means of uniform estimates on solutions of the time-difference equations, we establish the existence of weak solutions, and also discuss the uniqueness.

Improved Conditions for the Existence and Uniqueness of Solutions to the General Equality Constrained Quadratic Programming Problem

This paper presents an approach that directly utilizes the Hessian matrix to investigate the existence and uniqueness of global solutions for the ECQP problem. The novel features of this proposed algorithm are its uniqueness and faster rate of convergence to the solution. The merit of this algorithm is base on cost, accuracy and number of operations.

LOCAL EXISTENCE AND UNIQUENESS OF STRONG SOLUTIONS TO THE TWO DIMENSIONAL NONHOMOGENEOUS INCOMPRESSIBLE PRIMITIVE EQUATIONS

In this article,we study the initial boundary value problem of the two-dimensional nonhomogeneous incompressible primitive equations and obtain the local existence and uniqueness of strong solutions.The initial vacuum is allowed.

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.

AN EXISTENCE THEOREM OF POSITIVE SOLUTIONS FOR ELASTIC BEAM EQUATION WITH BOTH FIXED END-POINTS

By using the degree theory on cone an existence theorem of positive solution for a class of fourth-order two-point BVP's is obtained. This class of BVP's usually describes the deformation of the elastic beam with both fixed end-points.

Existence of solutions and positive solutions to a fourth-order two-point BVP with second derivative

Several existence theorems were established for a nonlinear fourth-order two-point boundary value problem with second derivative by using Leray-Schauder fixed point theorem, equivalent norm and technique on system of integral equations. The main conditions of our results are local. In other words, the existence of the solution can be determined by considering the height of the nonlinear term on a bounded set. This class of problems usually describes the equilibrium state of an elastic beam which is simply supported at both ends.

Existence and iteration of monotone positive solutions for a third-order two-point boundary value problem

The existence of nondecreasing positive solutions for the nonlinear third-order twopoint boundary value problem u′″（t） ＋ q（t）f（t,u（t）,u′（t）） = 0, 0 〈 t 〈 1, u（0） = u″（0） = u′（1） = 0 is studied. The iterative schemes for approximating the solutions are obtained by applying a monotone iterative method.

Existence and Uniqueness of Almost Periodic Solutions for Some Infinite Delay Integral Equations

In this paper, the existence and uniqueness of almost periodic solutions for some infinite delay integral equations are discussed. By using Krasnoselskii fixed point theorem,some new results are obtained.

EXISTENCE OF POSITIVE SOLUTIONS AND 1/c-GLOBAL ATTRACTIVITY OF A NONLINEAR DELAY DIFFERENCE EQUATION WITH VARIABLE COEFFICIENTS

The existence of positive solutions and the global attractivity of the difference equation Δy n=r ny nK-y n-l n K-cy n-l n are investigated. And some sufficient conditions are obtained,which greatly improve and extend the known results.

New Developments on Existence and Uniqueness of Solutions to Some Models in Atmospheric Dynamics

This survey is concerned with the new developments on existence and uniqueness of solutions of some basic models in atmospheric dynamics, such as two-and three-dimensional quasi-geostrophic models and three-dimensional balanced model. The main aim of this paper is to introduce some results about the global and local (with respect to time) existence of solutions given by the authors in recent years, but others' important contributions and the literature on this subject are also quoted. We discuss briefly the relationships among the existence and uniqueness, physical instability and computational instability. In the appendixes, some key mathematical techniques in obtaining our results are presented, which are of vital importance to other problems in geophysical fluid dynamics as well.

Existence of Multiple Positive Solutions on the Three Point Boundary Value Problems

In this paper, using fixed theorem in cones, the authors obtain the existence of multiple positive solutions on the following boundary value problem u＂＋a（t）f（u）=0,t∈[0,1],u（0）=0,au（η）^＊=u（1）.

ON THE EXISTENCE AND UNIQUENESS OF SOLUTION OF IMPLICIT HYBRID METHODS

In this paper the existence and uniqueness of the solution of implicit hybrid methods(IHMs)for solving the initial value problems(IVPs)of stiff ordinary differential equations(ODEs)is considered.We provide the coefficient condition and its judging criterion as well as the righthand condition to ensure the existing solution uniquely.

EXISTENCE AND UNIQUENESS OF PERIODIC SOLUTIONS FOR GRADIENT SYSTEMS IN FINITE DIMENSIONAL SPACES

This paper deals with an abstract periodic gradient system in which the gradient is taken with respect to a variable metric. We obtain an existence and uniqueness result via the application of a global inverse theorem.

Existence of Positive Solutions of Nonlinear NeutralEquations with Positive and Negative Coefficients

A class of nonlinear neutral equations with positive and negative coefficients is considered. Seveal conditions for existence of eventually positive solutions are obtained,and they extend and improve some of the criteria existing in literature. Our conditions are necessary and suffcient when all the coeffcients of the equations are constants.