In this article, by using theory of linear evolution system and Schauder fixed point theorem, we establish a sufficient result of exact null controllability for a non-autonomous functional evolution system with nonloc...In this article, by using theory of linear evolution system and Schauder fixed point theorem, we establish a sufficient result of exact null controllability for a non-autonomous functional evolution system with nonlocal conditions. In particular, the compactness condition or Lipschitz condition for the function g in the nonlocal conditions appearing in various literatures is not required here. An example is also provided to show an application of the obtained result.展开更多
In this article, we are concerned with the strong solutions of the coupled Navier-Stokes-Poisson equations for isentropic compressible fluids in a domain Ω R^3. We prove the local existence of unique strong solution...In this article, we are concerned with the strong solutions of the coupled Navier-Stokes-Poisson equations for isentropic compressible fluids in a domain Ω R^3. We prove the local existence of unique strong solutions provided that the initial data u0 and u0 satisfy a nature compatibility condition. The important point in this article is that we allow the initial vacuum: the initial density may vanish in an open subset of Ω. This is achieved by getting some uniform estimates and using a Schauder fixed point theorem.展开更多
This paper studies the existence of HSlder continuity of bidireetionally coupled generalised synchronisation (GS). Based on the slaving principle of synergetics and the modified system approach, it classifies the GS...This paper studies the existence of HSlder continuity of bidireetionally coupled generalised synchronisation (GS). Based on the slaving principle of synergetics and the modified system approach, it classifies the GS into several types. The existences of two main types of HSlder continuous bidirectionally coupled CS inertial manifolds are theoretically analysed and proved by using the Schauder fixed point theorem. Numerical simulations illustrate the theoretical results.展开更多
Let m be a positive integer and B be the unit ball of Rn (n≥2). We investigate the existence, uniqueness and the asymptotic behavior of a positive continuous solution to the following semilinear polyharmonic bounda...Let m be a positive integer and B be the unit ball of Rn (n≥2). We investigate the existence, uniqueness and the asymptotic behavior of a positive continuous solution to the following semilinear polyharmonic boundary value problem (-△)mu=a1(x)uα1+a2(x)uα2 , lim|x|→1 u(x) (1-|x|)m-1 =0, where α1,α2∈(-1, 1) and a1, a2 are two nonnegative measurable functions on B satisfying some appropriate assumptions related to Karamata regular variation theory.展开更多
A complex network consisting of chaotic systems is considered and the existence of the HSlder continuous gen- eralized synchronization in the network is studied. First, we divide nodes of the network into two parts ac...A complex network consisting of chaotic systems is considered and the existence of the HSlder continuous gen- eralized synchronization in the network is studied. First, we divide nodes of the network into two parts according to their dynamical behaviour. Then, based on the Schauder fixed point theorem, sufficient conditions for the existence of the generalized synchronization between them are derived. Moreover, the results are theoretically proved. Numerical simulations validate the theory.展开更多
This paper is to investigate the positive solutions of the systems of second-order ordinary differential equations with nonhomogeneous multi-point boundary conditions. By the lower and upper solutions method, Schauder...This paper is to investigate the positive solutions of the systems of second-order ordinary differential equations with nonhomogeneous multi-point boundary conditions. By the lower and upper solutions method, Schauder fixed point theorem and fixed point index theory, under certain conditions, it is proved that there exist appropriate regions of parameters in which the problem has at least two, at least one or no positive solution.展开更多
This paper deals with even order nonlinear differential equations. Applying the Schauder fixed point theorem and the Schwartz inequality technique, we give a criterion to ensure the existence and uniqueness of periodi...This paper deals with even order nonlinear differential equations. Applying the Schauder fixed point theorem and the Schwartz inequality technique, we give a criterion to ensure the existence and uniqueness of periodic solutions. This criterion is a complement of the well known Lazer type results.展开更多
By Fourier analysis techniques and Schauder fixed point theorem, we study the existence of periodic solutions for a class of even order differential equations with multiple delays. The result obtained is a generalizat...By Fourier analysis techniques and Schauder fixed point theorem, we study the existence of periodic solutions for a class of even order differential equations with multiple delays. The result obtained is a generalization of the results developed by W. Layton to the case of multiple delays.展开更多
In this article, we investigate the existence of positive solutions of a singular quasilinear elliptic system for which the cooperative structure is not required. The approach is based on the Schauder fixed point theo...In this article, we investigate the existence of positive solutions of a singular quasilinear elliptic system for which the cooperative structure is not required. The approach is based on the Schauder fixed point theorem combined with perturbation arguments that involve the singular terms.展开更多
In this paper, we study the anti-periodic solutions for 2n-th order differential equations. By using the Schauder's fixed point theorem, we present some new results about the existence and uniqueness of anti-periodic...In this paper, we study the anti-periodic solutions for 2n-th order differential equations. By using the Schauder's fixed point theorem, we present some new results about the existence and uniqueness of anti-periodic solutions for 2n-th order differential equations.展开更多
Existence of traveling wave solutions for some lattice differential equations is investigated. We prove that there exists c<sub>*</sub>>0 such that for each c≥c*</sub>, the systems und...Existence of traveling wave solutions for some lattice differential equations is investigated. We prove that there exists c<sub>*</sub>>0 such that for each c≥c*</sub>, the systems under consideration admit monotonic nondecreasing traveling waves.展开更多
Let T be a time scale such that 0, T ∈ T. By means of the Schauder fixed point theorem and analysis method, we establish some existence criteria for positive solutions of the m-point boundary value problem on time sc...Let T be a time scale such that 0, T ∈ T. By means of the Schauder fixed point theorem and analysis method, we establish some existence criteria for positive solutions of the m-point boundary value problem on time scales where α ∈ Ctd((O,T,[0,∞)),f∈ Ckd([0,∞)×[0,∞)),β,γ ∈[0,∞),ξi ∈(0,p(T).b,ai∈ (0,∞) (for i = 1,..., m - 2) are given constants satisfying some suitable hypotheses. We show that this problem has at least one positive solution for sufficiently small b 〉 0 and no solution for sufficiently large b. Our results are new even for the corresponding differential equation (T = R) and difference equation (T = Z).展开更多
The primary varicella-zoster virus(VzV)infection that causes chickenpox(also known as varicella),spreads quickly among people and,in severe circumstances,can cause to fever and encephalitis.In this paper,the Mittag-Le...The primary varicella-zoster virus(VzV)infection that causes chickenpox(also known as varicella),spreads quickly among people and,in severe circumstances,can cause to fever and encephalitis.In this paper,the Mittag-Leffler fractional operator is used to examine the mathematical representation of the vzV.Five fractional-order differential equations are created in terms of the disease's dynamical analysis such as S:Susceptible,V:Vaccinated,E:Exposed,I:Infectious and R:Recovered.We derive the existence criterion,positive solution,Hyers-Ulam stability,and boundedness of results in order to examine the suggested fractional-order model's wellposedness.Finally,some numerical examples for the VzV model of various fractional orders are shown with the aid of the generalized Adams-Bashforth-Moulton approach to show the viability of the obtained results.展开更多
This paper investigates a class of coupled systems of nonlinear fractional differential equations with three-point boundary conditions. Under suitable conditions the existence of solutions is obtained using the Schaud...This paper investigates a class of coupled systems of nonlinear fractional differential equations with three-point boundary conditions. Under suitable conditions the existence of solutions is obtained using the Schauder fixed point theorem.展开更多
The purpose of this paper is to investigate the existence of solutions to a nonlocal Cauchy problem for an evolution equation. The methods used here include the semigroup methods in proper spaces and Schauder's th...The purpose of this paper is to investigate the existence of solutions to a nonlocal Cauchy problem for an evolution equation. The methods used here include the semigroup methods in proper spaces and Schauder's theorem. And the results are applied to a system of nonlinear partial differential equations with nonlinear boundary conditions.展开更多
We study the periodic problem for differential inclusions in R^N.First we look for extremal periodicsolutions.Using techniques from multivalued analysis and a fixed point argument we establish an existencetheorem unde...We study the periodic problem for differential inclusions in R^N.First we look for extremal periodicsolutions.Using techniques from multivalued analysis and a fixed point argument we establish an existencetheorem under some general hypotheses.We also consider the“nonconvex periodic problem”under lowersemicontinuity hypotheses,and the“convex periodic problem”under general upper semicontinuity hypotheseson the multivalued vector field.For both problems,we prove existence theorems under very general hypotheses.Our approach extends existing results in the literature and appear to be the most general results on the nonconvexperiodic problem.展开更多
By means of the fixed point theorem and exponential dichotomy, in this paper we investigate the existence of almost periodic solutions to a class of ndimensional almost periodic systems, which is more general than the...By means of the fixed point theorem and exponential dichotomy, in this paper we investigate the existence of almost periodic solutions to a class of ndimensional almost periodic systems, which is more general than the systems in [1-2]. We generalize and improve some results in [3].展开更多
By means of Leray Schauder fixed point theorem, a kind of p-Laplacian functional differential equation with a deviating argument is studied. A new result on the existence of anti-periodic solution is obtained.
In this paper, with the elementary method, an existence proof on solutions to the nonlinear two-point boundary value problem is given under less restrictive conditions than [1]. This generalizes the result of [1] and ...In this paper, with the elementary method, an existence proof on solutions to the nonlinear two-point boundary value problem is given under less restrictive conditions than [1]. This generalizes the result of [1] and makes it as a corollary.展开更多
An existence and uniqueness of solutions for boundary value problemsare established, by employing a priori estimates for all solutions and the Schau-der fixed point theorem. Some of these results extend earlier result...An existence and uniqueness of solutions for boundary value problemsare established, by employing a priori estimates for all solutions and the Schau-der fixed point theorem. Some of these results extend earlier results due to Usmani (1979), Yang (1988), and Pei (1997).展开更多
基金supported by NSF of China (11171110)Shanghai Leading Academic Discipline Project (B407)
文摘In this article, by using theory of linear evolution system and Schauder fixed point theorem, we establish a sufficient result of exact null controllability for a non-autonomous functional evolution system with nonlocal conditions. In particular, the compactness condition or Lipschitz condition for the function g in the nonlocal conditions appearing in various literatures is not required here. An example is also provided to show an application of the obtained result.
基金Supported by National Natural Science Foundation of China-NSAF (10976026)
文摘In this article, we are concerned with the strong solutions of the coupled Navier-Stokes-Poisson equations for isentropic compressible fluids in a domain Ω R^3. We prove the local existence of unique strong solutions provided that the initial data u0 and u0 satisfy a nature compatibility condition. The important point in this article is that we allow the initial vacuum: the initial density may vanish in an open subset of Ω. This is achieved by getting some uniform estimates and using a Schauder fixed point theorem.
基金Project supported by the National Natural Science Foundation of China(Grants Nos.11002061 and 10901073)the Fundamental Research Funds for the Central Universities,China(Grant No.JUSRP10912)
文摘This paper studies the existence of HSlder continuity of bidireetionally coupled generalised synchronisation (GS). Based on the slaving principle of synergetics and the modified system approach, it classifies the GS into several types. The existences of two main types of HSlder continuous bidirectionally coupled CS inertial manifolds are theoretically analysed and proved by using the Schauder fixed point theorem. Numerical simulations illustrate the theoretical results.
文摘Let m be a positive integer and B be the unit ball of Rn (n≥2). We investigate the existence, uniqueness and the asymptotic behavior of a positive continuous solution to the following semilinear polyharmonic boundary value problem (-△)mu=a1(x)uα1+a2(x)uα2 , lim|x|→1 u(x) (1-|x|)m-1 =0, where α1,α2∈(-1, 1) and a1, a2 are two nonnegative measurable functions on B satisfying some appropriate assumptions related to Karamata regular variation theory.
基金Project supported by the National Natural Science Foundation of China (Grant Nos.11002061 and 10901073)the Fundamental Research Funds for the Central Universities,China (Grant No.JUSRP11117)
文摘A complex network consisting of chaotic systems is considered and the existence of the HSlder continuous gen- eralized synchronization in the network is studied. First, we divide nodes of the network into two parts according to their dynamical behaviour. Then, based on the Schauder fixed point theorem, sufficient conditions for the existence of the generalized synchronization between them are derived. Moreover, the results are theoretically proved. Numerical simulations validate the theory.
文摘This paper is to investigate the positive solutions of the systems of second-order ordinary differential equations with nonhomogeneous multi-point boundary conditions. By the lower and upper solutions method, Schauder fixed point theorem and fixed point index theory, under certain conditions, it is proved that there exist appropriate regions of parameters in which the problem has at least two, at least one or no positive solution.
文摘This paper deals with even order nonlinear differential equations. Applying the Schauder fixed point theorem and the Schwartz inequality technique, we give a criterion to ensure the existence and uniqueness of periodic solutions. This criterion is a complement of the well known Lazer type results.
基金The second author partially supported by NSFC (10571179, 10871203) GrantProgramfor New Century Excellent Talents in University of Ministry of Eduction of China
文摘By Fourier analysis techniques and Schauder fixed point theorem, we study the existence of periodic solutions for a class of even order differential equations with multiple delays. The result obtained is a generalization of the results developed by W. Layton to the case of multiple delays.
基金supported by the Europeanprogram Averroes-Erasmus Mundus(1872)
文摘In this article, we investigate the existence of positive solutions of a singular quasilinear elliptic system for which the cooperative structure is not required. The approach is based on the Schauder fixed point theorem combined with perturbation arguments that involve the singular terms.
文摘In this paper, we study the anti-periodic solutions for 2n-th order differential equations. By using the Schauder's fixed point theorem, we present some new results about the existence and uniqueness of anti-periodic solutions for 2n-th order differential equations.
文摘Existence of traveling wave solutions for some lattice differential equations is investigated. We prove that there exists c<sub>*</sub>>0 such that for each c≥c*</sub>, the systems under consideration admit monotonic nondecreasing traveling waves.
基金Supported by the NNSF of China(10571078)and the Teaching and Research Award Program for Outstanding Young Teachers in Higher Education Institutions of Ministry of Education of China,the Fundamental Research Fund for Physics and Mathematics of Lanzhou Uni
文摘Let T be a time scale such that 0, T ∈ T. By means of the Schauder fixed point theorem and analysis method, we establish some existence criteria for positive solutions of the m-point boundary value problem on time scales where α ∈ Ctd((O,T,[0,∞)),f∈ Ckd([0,∞)×[0,∞)),β,γ ∈[0,∞),ξi ∈(0,p(T).b,ai∈ (0,∞) (for i = 1,..., m - 2) are given constants satisfying some suitable hypotheses. We show that this problem has at least one positive solution for sufficiently small b 〉 0 and no solution for sufficiently large b. Our results are new even for the corresponding differential equation (T = R) and difference equation (T = Z).
文摘The primary varicella-zoster virus(VzV)infection that causes chickenpox(also known as varicella),spreads quickly among people and,in severe circumstances,can cause to fever and encephalitis.In this paper,the Mittag-Leffler fractional operator is used to examine the mathematical representation of the vzV.Five fractional-order differential equations are created in terms of the disease's dynamical analysis such as S:Susceptible,V:Vaccinated,E:Exposed,I:Infectious and R:Recovered.We derive the existence criterion,positive solution,Hyers-Ulam stability,and boundedness of results in order to examine the suggested fractional-order model's wellposedness.Finally,some numerical examples for the VzV model of various fractional orders are shown with the aid of the generalized Adams-Bashforth-Moulton approach to show the viability of the obtained results.
基金Supported by the Fundamental Research Foundations for the Central Universities (No.2010B08-2-1)in part by E-Institutes of Shanghai Municipal Education Commission (No.N.E03004)
文摘This paper investigates a class of coupled systems of nonlinear fractional differential equations with three-point boundary conditions. Under suitable conditions the existence of solutions is obtained using the Schauder fixed point theorem.
文摘The purpose of this paper is to investigate the existence of solutions to a nonlocal Cauchy problem for an evolution equation. The methods used here include the semigroup methods in proper spaces and Schauder's theorem. And the results are applied to a system of nonlinear partial differential equations with nonlinear boundary conditions.
文摘We study the periodic problem for differential inclusions in R^N.First we look for extremal periodicsolutions.Using techniques from multivalued analysis and a fixed point argument we establish an existencetheorem under some general hypotheses.We also consider the“nonconvex periodic problem”under lowersemicontinuity hypotheses,and the“convex periodic problem”under general upper semicontinuity hypotheseson the multivalued vector field.For both problems,we prove existence theorems under very general hypotheses.Our approach extends existing results in the literature and appear to be the most general results on the nonconvexperiodic problem.
基金The work is supported by the Natural Sciences Foundation of Hunan Province under Grant 03JJY3014 and the Item of the Government of Science and Technology of Yonezhou.
文摘By means of the fixed point theorem and exponential dichotomy, in this paper we investigate the existence of almost periodic solutions to a class of ndimensional almost periodic systems, which is more general than the systems in [1-2]. We generalize and improve some results in [3].
基金supported by Ministry of Education of Science and Technology of Important Projects (No.207047)Foundation of Anhui Educational Committee (KJ2010B353)Young Teacher’s Foundation of Anhui Normal University (2008xqn46)
文摘By means of Leray Schauder fixed point theorem, a kind of p-Laplacian functional differential equation with a deviating argument is studied. A new result on the existence of anti-periodic solution is obtained.
文摘In this paper, with the elementary method, an existence proof on solutions to the nonlinear two-point boundary value problem is given under less restrictive conditions than [1]. This generalizes the result of [1] and makes it as a corollary.
文摘An existence and uniqueness of solutions for boundary value problemsare established, by employing a priori estimates for all solutions and the Schau-der fixed point theorem. Some of these results extend earlier results due to Usmani (1979), Yang (1988), and Pei (1997).