This paper establishes an ordering contraction mapping principle for increasing mapping in partial ordering metric spaces, and applies it to prove the existence and uniqueness of fixed point for some nonlinear operato...This paper establishes an ordering contraction mapping principle for increasing mapping in partial ordering metric spaces, and applies it to prove the existence and uniqueness of fixed point for some nonlinear operators controlled by a linear operator and phi-concave operator in a partial ordering Banach space. Therefore, this two results are unified.展开更多
With the urgent need to resolve complex behaviors in nonlinear evolution equations,this study makes a contribution by establishing the local existence of solutions for Cauchy problems associated with equations of mixe...With the urgent need to resolve complex behaviors in nonlinear evolution equations,this study makes a contribution by establishing the local existence of solutions for Cauchy problems associated with equations of mixed types.Our primary contribution is the establishment of solution existence,illuminating the dynamics of these complex equations.To tackle this challenging problem,we construct an approximate solution sequence and apply the contraction mapping principle to rigorously prove local solution existence.Our results significantly advance the understanding of nonlinear evolution equations of mixed types.Furthermore,they provide a versatile,powerful approach for tackling analogous challenges across physics,engineering,and applied mathematics,making this work a valuable reference for researchers in these fields.展开更多
In this paper, we study a boundary value problem of nonlinear fractional dif- ferential equations of order q （1 〈 q 〈 2） with non-separated integral boundary conditions. Some new existence and uniqueness results a...In this paper, we study a boundary value problem of nonlinear fractional dif- ferential equations of order q （1 〈 q 〈 2） with non-separated integral boundary conditions. Some new existence and uniqueness results are obtained by using some standard fixed point theorems and Leray-Schauder degree theory. Some illustrative examples are also presented. We extend previous results even in the integer case q = 2.展开更多
In this paper, we study the existence, uniqueness, continuous dependence, Ulam stabilities and exponential stability of random impulsive semilineax differential equations under sufficient condition. The results are ob...In this paper, we study the existence, uniqueness, continuous dependence, Ulam stabilities and exponential stability of random impulsive semilineax differential equations under sufficient condition. The results are obtained by using the contraction mapping principle. Finally an example is given to illustrate the applications of the abstract results.展开更多
The authors consider Sidon sets of first kind. By comparing them with the Steinhaus sequence, they prove a local Khintchine-Kahane inequality on compact sets. As consequences, they prove the following results for Sido...The authors consider Sidon sets of first kind. By comparing them with the Steinhaus sequence, they prove a local Khintchine-Kahane inequality on compact sets. As consequences, they prove the following results for Sidon series taking values in a Banach space: the summability on a set of positive measure implies the almost everywhere convergence; the contraction principle of Billard-Kahane remains true for Sidon series. As applications, they extend a uniqueness theorem of Zygmund concerning lacunary Fourier series and an analytic continuation theorem of Hadamard concerning lacunary Taylor series. Some of their results still hold for Sidon sets of second kind.展开更多
In this paper,we study mixed non-linear fractional delay differential equations with integral boundary conditions.We obtain an equivalence result between the proposed problem and non-linear Fredholm integral equation ...In this paper,we study mixed non-linear fractional delay differential equations with integral boundary conditions.We obtain an equivalence result between the proposed problem and non-linear Fredholm integral equation of the second kind.Further,we establish existence and uniqueness of positive solutions for the problem using Guo-Krasnoseleskii's fixed point theorem and Banach contraction principle.展开更多
A nonlinear fractional integrodifferential equation with three-point fractional bound- ary conditions is studied in this paper, and some sufficient conditions for existence and u- niqueness of solutions for the equati...A nonlinear fractional integrodifferential equation with three-point fractional bound- ary conditions is studied in this paper, and some sufficient conditions for existence and u- niqueness of solutions for the equation are established by Krasnoselskii fixed point theorem and Banach contraction principle, respectively.展开更多
In this paper, we discuss the existence and uniqueness of mild solutions of random impulsive abstract neutral partial differential equations in a real separable Hilbert space. The results are obtained by using Leray-S...In this paper, we discuss the existence and uniqueness of mild solutions of random impulsive abstract neutral partial differential equations in a real separable Hilbert space. The results are obtained by using Leray-Schauder Alternative and Banach Contraction Principle.Finally an example is given to illustrate our problem.展开更多
The long-time behaviour of solution to chemotaxis-growth system with Neumann condition is considered in this paper. The approximate inertial manifolds of such equations are constructed based on the contraction princip...The long-time behaviour of solution to chemotaxis-growth system with Neumann condition is considered in this paper. The approximate inertial manifolds of such equations are constructed based on the contraction principle, and the orders of approximations of the manifolds to the global attractor are derived.展开更多
In physics, there are two main energy formulas. One is kinetic energy formula and the another is Einstein equation. But kinetic energy formula can only calculate low speed motion. Einstein equation can only calculate ...In physics, there are two main energy formulas. One is kinetic energy formula and the another is Einstein equation. But kinetic energy formula can only calculate low speed motion. Einstein equation can only calculate light speed motion. The two formulas are not unified. We hope to get a unified formula. But it didn’t work. According to the principle of Lorentz contraction, we generalize the contraction of length to the contraction of mass, and obtain a unified energy formula. This is the generalized Einstein equation and the new Einstein kinetic energy formula.展开更多
This paper is concerned with the existence and uniqueness of solution for a class of stochastic functional equation: X =φ(X), where φ: B → B and B is a Banach space consisted of all left-continuous, (■_t)-adapted ...This paper is concerned with the existence and uniqueness of solution for a class of stochastic functional equation: X =φ(X), where φ: B → B and B is a Banach space consisted of all left-continuous, (■_t)-adapted processes. Also, the main result is applied to some S.D.E (or S.I.E.). And the authors adopted some of the results in current research in the models of stochastic control recently. This paper proves the ekistence and uniquence and uniqueness of solution for stochastic functional equation. A series of corollaries are deduced from the special examples of the theorems in this paper.展开更多
Aim To investigate the existence of positive solutions for impulsive neutral differential equations. Methods The Banach contraction principle was used to establish our results. Results and Conclusion The results of...Aim To investigate the existence of positive solutions for impulsive neutral differential equations. Methods The Banach contraction principle was used to establish our results. Results and Conclusion The results of the existence of positive solutions for impulsive neutral differential equations are obtained.展开更多
In this article, using the contraction mapping principle and the shooting method, the authors obtain the existence and uniqueness of the local solution and the global solution to a class of quasilinear elliptic system...In this article, using the contraction mapping principle and the shooting method, the authors obtain the existence and uniqueness of the local solution and the global solution to a class of quasilinear elliptic systems with p-Laplacian as its principal. They also obtain the continuous dependence of the solutions on the boundary data.展开更多
The nonlinear Riemann problems were converted into nonlinear singular integral equ ations and the existence of the solution for the problem was proved by means of contract principle.
In this paper we discuss stochastic differential equations with a kind of periodic boundary value conditions（in sense of mean value）. Appealing to the decomposition of equations, the existence of solutions is obtain...In this paper we discuss stochastic differential equations with a kind of periodic boundary value conditions（in sense of mean value）. Appealing to the decomposition of equations, the existence of solutions is obtained by using the contraction mapping principle and Leray-Schauder fixed point theorem, respectively.展开更多
The aim of this paper is to study singular dynamics of solutions of Camassa-Holm equation. Based on the semigroup theory of linear operators and Banach contraction mapping principle, we prove the asymptotic stability ...The aim of this paper is to study singular dynamics of solutions of Camassa-Holm equation. Based on the semigroup theory of linear operators and Banach contraction mapping principle, we prove the asymptotic stability of the explicit singular solution of Camassa-Holm equation.展开更多
Let C be a nonempty bounded closed convex subset of a Banach space X, and T : C → C be uniformly L-Lipschitzian with L ≥ 1 and asymptotically pseudocontractive with a sequence {kn}(?)[1, ∞), limn→∞ kn = 1. Fix u ...Let C be a nonempty bounded closed convex subset of a Banach space X, and T : C → C be uniformly L-Lipschitzian with L ≥ 1 and asymptotically pseudocontractive with a sequence {kn}(?)[1, ∞), limn→∞ kn = 1. Fix u ∈ C. For each n ≥ 1, xn is a unique fixed point of the contraction Sn(x) = (1 - (tn)/(Lkn))u + (tn)/(Lkn)Tnx(?)x ∈ C, where {tn}(?)[0,1). Under suitable conditions, the strong convergence of the sequence{xn}to a fixed point of T is characterized.展开更多
In this paper,we construct an infinite family of approximate inertial manifolds for the Navier-Stokes equations.These manifolds provide higher and higher order approximations to the attractor.Our manifolds are constru...In this paper,we construct an infinite family of approximate inertial manifolds for the Navier-Stokes equations.These manifolds provide higher and higher order approximations to the attractor.Our manifolds are constructed by contraction principle and therefore can be easily approximated by simple explicit functions in real computations.展开更多
The iterative equation is an equality with an unknown function and its iterates,most of which found from references are a linear combination of those iterates.In this paper,we work on an iterative equation with multip...The iterative equation is an equality with an unknown function and its iterates,most of which found from references are a linear combination of those iterates.In this paper,we work on an iterative equation with multiplication of iterates of the unknown function.First,we use an exponential conjugation to reduce the equation on R+to the form of the linear combination on R,but those known results on the linear combination were obtained on a compact interval or a neighborhood near a fixed point.We use the Banach contraction principle to give the existence,uniqueness and continuous dependence of continuous solutions on R+that are Lipschitzian on their ranges,and construct its continuous solutions on R_(+)sewing piece by piece.We technically extend our results on R_(+)to R_(-)and show that none of the pairs of solutions obtained on R+and R_(-)can be combined at the origin to get a continuous solution of the equation on the whole R,but can extend those given on R+to obtain continuous solutions on the whole R.展开更多
文摘This paper establishes an ordering contraction mapping principle for increasing mapping in partial ordering metric spaces, and applies it to prove the existence and uniqueness of fixed point for some nonlinear operators controlled by a linear operator and phi-concave operator in a partial ordering Banach space. Therefore, this two results are unified.
基金Supported by the National Natural Science Foundation of China(12201368,62376252)Key Project of Natural Science Foundation of Zhejiang Province(LZ22F030003)Zhejiang Province Leading Geese Plan(2024C02G1123882,2024C01SA100795).
文摘With the urgent need to resolve complex behaviors in nonlinear evolution equations,this study makes a contribution by establishing the local existence of solutions for Cauchy problems associated with equations of mixed types.Our primary contribution is the establishment of solution existence,illuminating the dynamics of these complex equations.To tackle this challenging problem,we construct an approximate solution sequence and apply the contraction mapping principle to rigorously prove local solution existence.Our results significantly advance the understanding of nonlinear evolution equations of mixed types.Furthermore,they provide a versatile,powerful approach for tackling analogous challenges across physics,engineering,and applied mathematics,making this work a valuable reference for researchers in these fields.
文摘In this paper, we study a boundary value problem of nonlinear fractional dif- ferential equations of order q （1 〈 q 〈 2） with non-separated integral boundary conditions. Some new existence and uniqueness results are obtained by using some standard fixed point theorems and Leray-Schauder degree theory. Some illustrative examples are also presented. We extend previous results even in the integer case q = 2.
文摘In this paper, we study the existence, uniqueness, continuous dependence, Ulam stabilities and exponential stability of random impulsive semilineax differential equations under sufficient condition. The results are obtained by using the contraction mapping principle. Finally an example is given to illustrate the applications of the abstract results.
文摘The authors consider Sidon sets of first kind. By comparing them with the Steinhaus sequence, they prove a local Khintchine-Kahane inequality on compact sets. As consequences, they prove the following results for Sidon series taking values in a Banach space: the summability on a set of positive measure implies the almost everywhere convergence; the contraction principle of Billard-Kahane remains true for Sidon series. As applications, they extend a uniqueness theorem of Zygmund concerning lacunary Fourier series and an analytic continuation theorem of Hadamard concerning lacunary Taylor series. Some of their results still hold for Sidon sets of second kind.
基金Supported by Council of Scientific and Industrial Research-Human Resource Development Group(CSIR-HRDG)(Grant No.09/0990(11223)/2021-EMR-I)。
文摘In this paper,we study mixed non-linear fractional delay differential equations with integral boundary conditions.We obtain an equivalence result between the proposed problem and non-linear Fredholm integral equation of the second kind.Further,we establish existence and uniqueness of positive solutions for the problem using Guo-Krasnoseleskii's fixed point theorem and Banach contraction principle.
文摘A nonlinear fractional integrodifferential equation with three-point fractional bound- ary conditions is studied in this paper, and some sufficient conditions for existence and u- niqueness of solutions for the equation are established by Krasnoselskii fixed point theorem and Banach contraction principle, respectively.
文摘In this paper, we discuss the existence and uniqueness of mild solutions of random impulsive abstract neutral partial differential equations in a real separable Hilbert space. The results are obtained by using Leray-Schauder Alternative and Banach Contraction Principle.Finally an example is given to illustrate our problem.
基金Supported by the National Natural Science Foundation of China (Grant No. 11071177)the Natural Science Foundation of Sichuan Education Department (No. 11ZA102)
文摘The long-time behaviour of solution to chemotaxis-growth system with Neumann condition is considered in this paper. The approximate inertial manifolds of such equations are constructed based on the contraction principle, and the orders of approximations of the manifolds to the global attractor are derived.
文摘In physics, there are two main energy formulas. One is kinetic energy formula and the another is Einstein equation. But kinetic energy formula can only calculate low speed motion. Einstein equation can only calculate light speed motion. The two formulas are not unified. We hope to get a unified formula. But it didn’t work. According to the principle of Lorentz contraction, we generalize the contraction of length to the contraction of mass, and obtain a unified energy formula. This is the generalized Einstein equation and the new Einstein kinetic energy formula.
文摘This paper is concerned with the existence and uniqueness of solution for a class of stochastic functional equation: X =φ(X), where φ: B → B and B is a Banach space consisted of all left-continuous, (■_t)-adapted processes. Also, the main result is applied to some S.D.E (or S.I.E.). And the authors adopted some of the results in current research in the models of stochastic control recently. This paper proves the ekistence and uniquence and uniqueness of solution for stochastic functional equation. A series of corollaries are deduced from the special examples of the theorems in this paper.
文摘Aim To investigate the existence of positive solutions for impulsive neutral differential equations. Methods The Banach contraction principle was used to establish our results. Results and Conclusion The results of the existence of positive solutions for impulsive neutral differential equations are obtained.
文摘In this article, using the contraction mapping principle and the shooting method, the authors obtain the existence and uniqueness of the local solution and the global solution to a class of quasilinear elliptic systems with p-Laplacian as its principal. They also obtain the continuous dependence of the solutions on the boundary data.
文摘The nonlinear Riemann problems were converted into nonlinear singular integral equ ations and the existence of the solution for the problem was proved by means of contract principle.
基金The NSF(1308085MA01,1508085QA01)of Anhui Provincethe Provincial Natural Science Research Project(KJ2014A010)of Anhui Colleges+1 种基金the National Natural Science Youth Foundation(11301004)of ChinaOutstanding Youth Key Foundation(2013SQRL087ZD)of Colleges and Universities in Anhui Province
文摘In this paper we discuss stochastic differential equations with a kind of periodic boundary value conditions（in sense of mean value）. Appealing to the decomposition of equations, the existence of solutions is obtained by using the contraction mapping principle and Leray-Schauder fixed point theorem, respectively.
文摘The aim of this paper is to study singular dynamics of solutions of Camassa-Holm equation. Based on the semigroup theory of linear operators and Banach contraction mapping principle, we prove the asymptotic stability of the explicit singular solution of Camassa-Holm equation.
基金The Teaching and Research Award Fund for Outstanding Young Teachers in Higher Education Institutions of MOE, China, and The Dawn Program Fund in Shanghai.
文摘Let C be a nonempty bounded closed convex subset of a Banach space X, and T : C → C be uniformly L-Lipschitzian with L ≥ 1 and asymptotically pseudocontractive with a sequence {kn}(?)[1, ∞), limn→∞ kn = 1. Fix u ∈ C. For each n ≥ 1, xn is a unique fixed point of the contraction Sn(x) = (1 - (tn)/(Lkn))u + (tn)/(Lkn)Tnx(?)x ∈ C, where {tn}(?)[0,1). Under suitable conditions, the strong convergence of the sequence{xn}to a fixed point of T is characterized.
文摘In this paper,we construct an infinite family of approximate inertial manifolds for the Navier-Stokes equations.These manifolds provide higher and higher order approximations to the attractor.Our manifolds are constructed by contraction principle and therefore can be easily approximated by simple explicit functions in real computations.
基金supported by National Institute of Technology Karnataka Surathkal through Senior Research Fellowship and Indian Statistical Institute Bangalore in the form of a Visiting Scientist position through the Jagadish Chandra Bose Fellowship of Professor Badekkila Venkataramana Rajarama Bhatsupported by Science and Engineering Research Board,Department of Science and Technology,Government of India(Grant No.ECR/2017/000765)supported by National Natural Science Foundation of China(Grant Nos.11831012,12171336 and 11821001).
文摘The iterative equation is an equality with an unknown function and its iterates,most of which found from references are a linear combination of those iterates.In this paper,we work on an iterative equation with multiplication of iterates of the unknown function.First,we use an exponential conjugation to reduce the equation on R+to the form of the linear combination on R,but those known results on the linear combination were obtained on a compact interval or a neighborhood near a fixed point.We use the Banach contraction principle to give the existence,uniqueness and continuous dependence of continuous solutions on R+that are Lipschitzian on their ranges,and construct its continuous solutions on R_(+)sewing piece by piece.We technically extend our results on R_(+)to R_(-)and show that none of the pairs of solutions obtained on R+and R_(-)can be combined at the origin to get a continuous solution of the equation on the whole R,but can extend those given on R+to obtain continuous solutions on the whole R.
