Fractional Differential Equations with Anti-Periodic Boundary Conditions

We are concerned with the existence of solutions of a class of fractional differential equations with anti-periodic boundary conditions involving the Caputo fractional derivative. We give two results: the first is based on Banach's fixed-point theorem, and the second is based on Schauder's fixed-point theorem.     

Existence and nonexistence of positive solutions for a class of nth-order three-point boundary value problems in Banach spaces

By using the fixed-point principle in cone and the fixed-point index theory for strict-set-contraction operator, this paper investigates the existence, nonexistence, and multiplicity of positive solutions for a class of nonlinear three-point boundary value problems of nth-order differential equations in ordered Banach spaces. In addition, an example is included to demonstrate the main results.     

Anticipated backward stochastic differential equations driven by the Teugels martingales

In this paper, a class of anticipated backward stochastic differential equations driven by Teugels martingales associated with Lévy process is investigated. We obtain the existence and uniqueness of solutions to these equations by means of the fixed-point theorem. We show that a comparison theorem for this type of ABSDEs also holds under some slight stronger conditions.     

Integer solution of a set of bilinear equations

An efficient method for a design of transmultiplexer filters is suggested. The perfect reconstruction conditions lead to the bilinear equations for FIR filters coefficients. The method of solving these equations results from the presented theorem. Usefulness of the algorithm in fixed-point arithmetic is the crucial issue. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A Theorem for Numerical Verification on Local Uniqueness of Solutions to Fixed-Point Equations

We give a theoretical result with respect to numerical verification of existence and local uniqueness of solutions to fixed-point equations which are supposed to have Fréchet differentiable operators. The theorem is based on Banach's fixed-point theorem and gives sufficient conditions in order that a given set of functions includes a unique solution to the fixed-point equation. The conditions are formulated to apply readily to numerical verification methods.

We already derived such a theorem in [11 N. Yamamoto ( 1998 ). A numerical verification method for solutions of boundary value problems with local uniqueness by Banach's fixed-point theorem . SIAM J. Numer. Anal. 35 : 2004 – 2013 .[Crossref] , [Google Scholar]], which is suitable to Nakao's methods on numerical verification for PDEs. The present theorem has a more general form and one may apply it to many kinds of differential equations and integral equations which can be transformed into fixed-point equations.     

An example of application of the Nielsen theory to integro-differential equations

A new nontrivial example of an application of the Nielsen fixed-point theory is presented, this time, to integro-differential equations. The emphasis is on the parameter space so that no subdomain becomes invariant under the related solution (Hammerstein) operator. Thus, at least three (harmonic) periodic solutions are established to a planar integro-differential system.

     

Some results on second-order neutral functional differential equations with infinite distributed delay

In this paper, we consider two types of second-order neutral functional differential equations with infinite distributed delay. By choosing available operators and applying Krasnoselskii’s fixed-point theorem, we obtain sufficient conditions for the existence of periodic solutions to such equations.     

Periodic boundary value problems of second-order impulsive differential equations

This paper discusses periodic boundary value problems of second-order impulsive differential equations. By using Schaeffer’s fixed-point theorem and monotone iterative technique, some existence results are obtained.     

Existence and nonexistence of positive solutions for a class of third order BVP with integral boundary conditions in Banach spaces

This paper investigates the existence, nonexistence, and multiplicity of positive solutions for a class of nonlinear boundary-value problems of third order differential equations with integral boundary conditions in ordered Banach spaces by means of fixed-point principle in cone and the fixed-point index theory for strict set contraction operator. In addition, an example is worked out to demonstrate the main results.     

Existence of two solutions of m-point boundary value problem for second order dynamic equations on time scales

In this paper, by means of a new twin fixed-point theorem in a cone, the existence of at least two positive solutions of m-point boundary value problem for second order dynamic equations on time scales is considered.     

Existence and uniqueness of fuzzy solution for the nonlinear fuzzy integrodifferential equations

In this paper, existence and uniqueness of fuzzy solution for the nonlinear fuzzy integrodifferential equations is established via Banach fixed-point analysis approach and using the fuzzy number whose values are normal, convex, upper semicontinuous and compactly supported interval in E_N.     

MULTIPLE POSITIVE SOLUTIONS TO BOUNDARY VALUE PROBLEMS OF DELAY DIFFERENTIAL EQUATIONS WITH DENUMBERABLE SINGULARITIES ON INFINITE INTERVAL

This paper deals with the existence of denumberable positive solutions to boundary value problems of delay differential equations with denumberable singularities on infinite intervals. By the fixed-point index theory and a new fixed-point theorem in cones, the existence of denumberable positive solutions is obtained under some suitable growth conditions imposed on the nonlinear term.     

Triple positive solutions of boundary value problems for p-Laplacian dynamic equations on time scales

A new triple fixed-point theorem is applied to investigate the existence of at least three positive solutions of boundary value problems for p-Laplacian dynamic equations on time scales.     

Applications of the fixed point index in Menger PN-spaces

In this paper, applications of the fixed-point index of a nonlinear operator in Menger PN-spaces are given. Theorems on the existence of fixed points of a compact continuous operator are obtained. At the same time, the existence of the solution of a class of differential equations in a complete Menger PN-space is studied, and the theorem on the existence of the solution of a class of differential equations is obtained.     

不动点定理在奇摄动非线性初值问题的套层解中的应用

Singularperturbationofnonlinearboundaryvalueproblemswhichhavedoubleboundarylayerpropertieswerediscussedbysomeauthorsusingthemethodofdifferentialinequali ties[1 ] -[3 ] .Nonlinearboundaryvalueproblemswhichhavenotdoubleboundarylayerpropertieswerediscussedbysomeauthorsusingthemethodofthefixed_pointtheorem[4] -[6 ] .Inthispa perwewillusethefixed_pointtheoremtodiscussthethirdorderdifferentialequationswhichhavedoubleinitiallayer.Weconsiderthefollowingproblem .ε4y =h(t,y,εy′,ε2 y″,ε) ,t∈ [0 ,T…     

On some fixed-point theorems for generalized contractions and their perturbations

The aim of this paper is to prove a collection of fixed-point theorems for mappings which can be roughly called generalized contractions or their perturbations. In particular, we are going to consider operators (single-valued or multi-valued) in Banach spaces with a quasimodulus, in hyperconvex subsets of normed spaces, or finally in non-Archimedean spaces. A particular attention will be paid to Krasnoselskii-type fixed-point theorems as well as to a Schaefer-type fixed-point theorem. Some applications to nonlinear functional-integral equations will be given. Our results extend and complement some commonly known theorems.     

Weak solutions to the stationary quantum drift-diffusion model

The existence of weak solutions to the stationary quantum drift-diffusion equations for semiconductor devices is investigated. The proof is based on minimization procedure of non-linear functional and Schauder fixed-point theorem. Furthermore, the semiclassical limit ε→0 from the quantum drift-diffusion model to the classical drift-diffusion model is discussed.     

POSITIVE SOLUTIONS FOR p-LAPLACIAN DYNAMIC EQUATIONS ON TIME SCALES

The three-point boundary value problems of p-Laplacian dynamic equations on time scales are investigated. By using Krasnosel＇skii＇s fixed-point theorem and fixed-point index theorem, criteria are achieved for the existence of at least one, two or 2n positive solutions. Furthermore, some examples are included to illustrate the main theorems.     

Eigenvalue problems and fixed point theorems for a class of positive nonlinear operators

We study the eigenvalue problems for a class of positive nonlinear operators defined on a cone in a Banach space. Using projective metric techniques and Schauder’s fixed-point theorem, we establish existence, uniqueness, monotonicity and continuity results for the eigensolutions. Moreover, the method leads to a result on the existence of a unique fixed point of the operator. Applications to nonlinear boundary-value problems, to differential delay equations and to matrix equations are considered.      

Banach空间中的半线性发展方程

讨论了Banach空间X中带有非局部条件的半线性发展方程．在g失去紧性的条件下，利用L^p（I；X）空间中的不动点定理，对边值问题适度解的存在性做了研究，完善和推广了已有结论．最后给出一个在偏微分方程中的例子．