SOME NEW EXTENSIONS OF EDELSTEIN-SUZUKI-TYPE FIXED POINT THEOREM TO G-METRIC AND G-CONE METRIC SPACES

In this paper, we prove some fixed point theorems for generalized contractions in the setting of G-metric spaces. Our results extend a result of Edelstein [M. Edelstein, On fixed and periodic points under contractive mappings, J. London Math. Soc., 37 （1962）, 74-79] and a result of Suzuki [T. Suzuki, A new type of fixed point theorem in metric spaces, Nonlinear Anal., 71 （2009）, 5313-5317]. We prove, also, a fixed point theorem in the setting of G-cone metric spaces.

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.

New Fixed Point Results of Generalized g-Quasi-Contractions in Cone b-Metric Spaces Over Banach Algebras

In this paper, we introduce the concept of generalized g-quasi-contractions in the setting of cone b-metric spaces over Banach algebras. By omitting the assump- tion of normality we establish common fixed point theorems for the generalized g- quasi-contractions with the spectral radius r（λ） of the g-quasi-contractive constant vector λ satisfying r（λ） ∈[0,1） in the setting of cone b-metric spaces over Banach al- gebras, where the coefficient s satisfies s ≥ 1. The main results generalize, extend and unify several well-known comparable results in the literature.

Existence of Positive Solutions for Higher-Order Four-Point Boundary Value Problems with a p-Laplacian Operator

A class of higher-order four-point boundary value problems with a p-Laplacian operator is studied. By use of a fixed point theorem in cones, sufficient conditions for the existence of positive solutions for the boundary value problems are obtained.

Existence and Uniqueness of Positive Solution for 2mth-Order Nonlinear Differential Equation with Boundary Conditions

In this paper, we study the existence and uniqueness of positive solution for 2mth-order nonlinear differential equation with boundary conditions, by using the fixed point theorems on compression and expansion of cones.

Positive Solutions of Four-order Dierence Equations with Two Point Boundary Value Problems

In this paper,by using the Krasnoselskii xed point theorem,we prove the existence one or multiple of positive solutions of fourth-ordernonlinear dierence equations with two point boundary value problem.

EXISTENCE THEOREMS OF SOLUTIONS FOR NONLINEAR IMPULSIVE VOLTERRA INTEGRAL EQUATIONS IN BANACH SPACES

In this paper,the Monch fixed point theorem and an impulsive integral inequality is used to prove some existence theorems of solutions for nonlinear impulsive Volterra integral equations in Banach spaces that improve and extend the previous results.

Existence of Positive Solutions for Boundary Value Problem of Nonlinear Fractional <i>q</i>-Difference Equation

In this paper, we investigate the existence of positive solutions for a class of nonlinear q-fractional boundary value problem. By using some fixed point theorems on cone, some existence results of positive solutions are obtained.

EXISTENCE OF POSITIVE SOLUTIONS FOR p-LAPLACIAN SINGULAR BOUNDARY VALUE PROBLEMS OF FUNCTIONAL DIFFERENTIAL EQUATION

In this paper,the boundary value problems of p-Laplacian functional differential equation are studied.By using a fixed point theorem in cones,some criteria for the existence of positive solutions are given.

RADIAL CONVEX SOLUTIONS OF A SINGULAR DIRICHLET PROBLEM WITH THE MEAN CURVATURE OPERATOR IN MINKOWSKI SPACE

In this paper, we study the existence of nontrivial radial convex solutions of a singular Dirichlet problem involving the mean curvature operator in Minkowski space. The proof is based on a well-known fixed point theorem in cones. We deal with more general nonlinear term than those in the literature.

On the Existence of Time-periodic Solution to the Compressible Heat-conducting Navier-Stokes Equations

We study in this article the compressible heat-conducting Navier-Stokes equations in periodic domain driven by a time-periodic external force. The existence of the strong time-periodic solution is established by a new approach. First, we reformulate the system and consider some decay estimates of the linearized system.Under some smallness and symmetry assumptions on the external force, the existence of the time-periodic solution of the linearized system is then identi?ed as the ?xed point of a Poincare′ map which is obtained by the Tychonoff ?xed point theorem.Although the Tychonoff ?xed point theorem cannot directly ensure the uniqueness,but we could construct a set-valued function, the ?xed point of which is the timeperiodic solution of the original system. At last, the existence of the ?xed point is obtained by the Kakutani ?xed point theorem. In addition, the uniqueness of timeperiodic solution is also studied.

Existence of Positive Solutions to Boundary Value Problem for a Nonlinear Fractional Differential Equation

In this paper,we study a Dirichlet-type boundary value problem(BVP) of nonlinear fractional differential equation with an order α∈(3,4],where the fractional derivative D~α_(o^+)is the standard Riemann-Liouville fractional derivative.By constructing the Green function and investigating its properties,we obtain some criteria for the existence of one positive solution and two positive solutions for the above BVP.The Krasnosel'skii fixedpoint theorem in cones is used here.We also give an example to illustrate the applicability of our results.

Three positive doubly periodic solutions of a nonlinear telegraph system

This paper studies existence of at least three positive doubly periodic solutions of a coupled nonlinear telegraph system with doubly periodic boundary conditions. First, by using the Green function and maximum principle, existence of solutions of a nonlinear telegraph system is equivalent to existence of fixed points of an operator. By imposing growth conditions on the nonlinearities, existence of at least three fixed points in cone is obtained by using the Leggett-Williams fixed point theorem to cones in ordered Banach spaces. In other words, there exist at least three positive doubly periodic solutions of nonlinear telegraph system.

POSITIVE SOLUTIONS TO AN m-POINT BOUNDARY VALUE PROBLEM

The existence of positive solutions for second order m-point boundary value problemx″-q(t)f(x,x′)x′=0, x(0)= m i=2 b ix(ξ i),x′(1)=αx′(0)are investigated,where ξ i,b i and α are constants satisfying 0=ξ 1<ξ 2<...<ξ m-1 <ξ m=1,b i≥0 for i=2,...,m with β∶= m i=2 b i∈[0,1), and α>1. Our approach is based on the fixed point theorem in cones.

MULTIPLICITY OF POSITIVE PERIODIC SOLUTIONS TO SECOND ORDER SINGULAR DIFFERENTIAL SYSTEMS

In this article, the author is devoted to establish the multiplicity of positive periodic solutions to second-order singular differential systems. It is proved that such a problem has at least two positive solutions under our reasonable conditions. The proof relies on a nonlinear alternative of Leray- Schauder type and Krasnoselskii fixed point theorem in cones.

Positive solutions to (n-1,1) m-point boundary value problems with dependence on the first order derivative

Using the extension of Krasnoselskii＇s fixed point theorem in a cone, we prove the existence of at least one positive solution to the nonlinear nth order m-point boundary value problem with dependence on the first order derivative. The associated Green＇s function for the nth order m-point boundary value problem is given, and growth conditions are imposed on the nonlinear term f which ensures the existence of at least one positive solution. A simple example is presented to illustrate applications of the obtained results.

On No-Node Solutions of the Lazer-McKenna Suspension Bridge Models

In this paper, we are concerned with the existence and multiplicity of no-node solutions of the Lazer-McKenna suspension bridge models by using the fixed point theorem in a cone.

Positive periodic solutions of higher-dimensional nonlinear functional difference equations

In this paper, we apply a cone theoretic fixed point theorem to obtain sufficient conditions for the existence of multiple positive periodic solutions to the higher-dimensional functional difference equations of the form:x(n+ 1) =A(n)x(n) +λh(n)f(x(n- τ(n))), n∈ Z.