In this paper we study a nonstationary Oseen model for a generalized Newtonian incompressible fluid with a time periodic condition and a multivalued,nonmonotone friction law.First,a variational formulation of the mode...In this paper we study a nonstationary Oseen model for a generalized Newtonian incompressible fluid with a time periodic condition and a multivalued,nonmonotone friction law.First,a variational formulation of the model is obtained;that is a nonlinear boundary hemivariational inequality of parabolic type for the velocity field.Then,an abstract first-order evolutionary hemivariational inequality in the framework of an evolution triple of spaces is investigated.Under mild assumptions,the nonemptiness and weak compactness of the set of periodic solutions to the abstract inequality are proven.Furthermore,a uniqueness theorem for the abstract inequality is established by using a monotonicity argument.Finally,we employ the theoretical results to examine the nonstationary Oseen model.展开更多
The existence of T_periodic solutions of the nonlinear system with multiple delays is studied. By using the topological degree method, sufficient conditions are obtained for the existence of T_periodic solutions. As a...The existence of T_periodic solutions of the nonlinear system with multiple delays is studied. By using the topological degree method, sufficient conditions are obtained for the existence of T_periodic solutions. As an application, the existence of positive periodic solution for a logarithmic population model is established under some conditions.展开更多
A periodically homoclinic solution and some rogue wave solutions of (1+1)-dimensional Boussinesq equation are obtained via the limit behavior of parameters and different polynomial functions. Besides, the mathematics ...A periodically homoclinic solution and some rogue wave solutions of (1+1)-dimensional Boussinesq equation are obtained via the limit behavior of parameters and different polynomial functions. Besides, the mathematics reasons for different spatiotemporal structures of rogue waves are analyzed using the extreme value theory of the two-variables function. The diversity of spatiotemporal structures not only depends on the disturbance parameter u0 </sub>but also has a relationship with the other parameters c<sub>0</sub>, α, β.展开更多
The existence of positive solutions to second-order periodic BVPs-u"+Mu =j(t, u),t(0) = u(2π),u’(0) = "(2π) and u"+ Mu = I(t, u), u(0) = u(2π), u’(0) = u’(2π)is proved by a simple appliCation of ...The existence of positive solutions to second-order periodic BVPs-u"+Mu =j(t, u),t(0) = u(2π),u’(0) = "(2π) and u"+ Mu = I(t, u), u(0) = u(2π), u’(0) = u’(2π)is proved by a simple appliCation of a Fixed point Theorem in cones due to Krasnoselskii.展开更多
This paper deals with the existence of positive periodic solutions for a kind of nonautonomous Volterra intergo-differential equations by employing the Krasnoselskii fixed point theorem. Applying the general theorems ...This paper deals with the existence of positive periodic solutions for a kind of nonautonomous Volterra intergo-differential equations by employing the Krasnoselskii fixed point theorem. Applying the general theorems established to several biomathematical models, the paper improves some previous results and obtains some new results.展开更多
In this paper, the existence of periodic solutions for a time dependent agestructured population model is studied. The averaged net reproductive number is introduced as the main parameter to determine the dynamical be...In this paper, the existence of periodic solutions for a time dependent agestructured population model is studied. The averaged net reproductive number is introduced as the main parameter to determine the dynamical behaviors of the model. Theexistence of a globa.l parameterized branch of periodic solutions of the model is obtained byusing the contracting mapping theorem in a periodic and continuous function space. Theglobal stability of the trivial equilibrium is studied and a very practical stability criteriafor the model is obtained. The dynamics of the linear time-periodic model is similar tothat of the linear model.展开更多
Considering a decomposition R2N=A⊕B of R2N , we prove in this work, the existence of at least (1+dimA) geometrically distinct periodic solutions for the first-order Hamiltonian system Jx'(t)+H'(t,x(t))+e(t)=0...Considering a decomposition R2N=A⊕B of R2N , we prove in this work, the existence of at least (1+dimA) geometrically distinct periodic solutions for the first-order Hamiltonian system Jx'(t)+H'(t,x(t))+e(t)=0 when the Hamiltonian H(t,u+v) is periodic in (t,u) and its growth at infinity in v is at most like or faster than |v|a, 0≤ae is a forcing term. For the proof, we use the Least Action Principle and a Generalized Saddle Point Theorem.展开更多
Based on Mansevich-Mawhin continuation theorem and some analysis skill,some sufficient conditions for the existence of periodic solutions for mixed type p-Laplacian equation with deviating arguments are established,...Based on Mansevich-Mawhin continuation theorem and some analysis skill,some sufficient conditions for the existence of periodic solutions for mixed type p-Laplacian equation with deviating arguments are established,which are complement of previously known results.展开更多
The global phase portrait describes the qualitative behaviour of the solution set of a nonlinear ordinary differential equation, for all time. In general, this is as close as we can come to solving nonlinear systems. ...The global phase portrait describes the qualitative behaviour of the solution set of a nonlinear ordinary differential equation, for all time. In general, this is as close as we can come to solving nonlinear systems. In this research work we study the dynamics of a bead sliding on a wire with a given specified shape. A long wire is bent into the shape of a curve with equation z = f (x) in a fixed vertical plane. We consider two cases, namely without friction and with friction, specifically for the cubic shape f (x) = x3−x . We derive the corresponding differential equation of motion representing the dynamics of the bead. We then study the resulting second order nonlinear ordinary differential equations, by performing simulations using MathCAD 14. Our main interest is to investigate the existence of periodic solutions for this dynamics in the neighbourhood of the critical points. Our results show clearly that periodic solutions do indeed exist for the frictionless case, as the phase portraits exhibit isolated limit cycles in the phase plane. For the case with friction, the phase portrait depicts a spiral sink, spiraling into the critical point.展开更多
For functional difference equations with unbounded delay,we characterized the existence of totally stable and asymptotically almost periodic solution by using stability properties of a bounded solution in a certain li...For functional difference equations with unbounded delay,we characterized the existence of totally stable and asymptotically almost periodic solution by using stability properties of a bounded solution in a certain limiting equation.展开更多
By means of Mawhin's continuation theorem,we study a kind of lie'nard functional differential equations:x"(t)+f(x(t))x'(t)+g(t,x(t-τ(t))) = e(t).Some new results on the existence and uniqueness of pe...By means of Mawhin's continuation theorem,we study a kind of lie'nard functional differential equations:x"(t)+f(x(t))x'(t)+g(t,x(t-τ(t))) = e(t).Some new results on the existence and uniqueness of periodic solutions are obtained.展开更多
By establishing a comparison result and using monotone iterative methods, the theorem of existence for minimal and maximal solutions of periodic boundary value problems for second_order nonlinear integro_differential ...By establishing a comparison result and using monotone iterative methods, the theorem of existence for minimal and maximal solutions of periodic boundary value problems for second_order nonlinear integro_differential equations in Banach spaces is proved.展开更多
We give sufficient conditions ensuring the existence and uniqueness of an Eberlein-weakly almost periodic solution to the following linear equation dx/dt(t) = A(t)x(t) + f(t) in a Banach space X, where (A(t)) t ∈□ i...We give sufficient conditions ensuring the existence and uniqueness of an Eberlein-weakly almost periodic solution to the following linear equation dx/dt(t) = A(t)x(t) + f(t) in a Banach space X, where (A(t)) t ∈□ is a family of infinitesimal generators such that for all t ∈□, A(t + T) = A(t) for some T > 0, for which the homogeneuous linear equation dx/dt(t) = A(t)x(t) is well posed, stable and has an exponential dichotomy, and f:□ →X is Eberlein-weakly amost periodic.展开更多
In this paper, we study the generalized coupled Hirota Satsuma KdV system by using the new generalizedtransformation in homogeneous balance method. As a result, many explicit exact solutions, which contain new solitar...In this paper, we study the generalized coupled Hirota Satsuma KdV system by using the new generalizedtransformation in homogeneous balance method. As a result, many explicit exact solutions, which contain new solitarywave solutions, periodic wave solutions, and the combined formal solitary wave solutions, and periodic wave solutions,are obtained.展开更多
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.
In this paper, we consider an almost periodic system which includes a system of the type , where k is a positive integer, aij are almost periodic in n and satisfy aij(n)≥0 for i≠j,? for 1≤j≤m. In the special case ...In this paper, we consider an almost periodic system which includes a system of the type , where k is a positive integer, aij are almost periodic in n and satisfy aij(n)≥0 for i≠j,? for 1≤j≤m. In the special case where aij(n) are constant functions, above system is a mathematical model of gas dynamics and was treated by T. Carleman and R. D. Jenks for differential systems. In the main theorem, we show that if the m X m matrix (aij(n)) is irreducible, then there exists a positive almost periodic solution which is unique and has some stability. Moreover, we can see that this result gives R. D. Jenks’ result for differential model in the case where aij(n) are constant functions. In Section 3, we consider the linear system with variable cofficients . Even in nonlinear problems, this linear system plays an important role, as their variational equations, and it is requested to determine the uniform asymptotically stability of the zero solution from the information about A(n). In order to obtain the existence of almost periodic solutions of both linear and nonlinear almost periodic discrete systems: above linear system and? for 1≤i≤m, respectively, we shall consider between certain stability properties, which are referred to as uniformly asymptotically stable, and the diagonal dominance matrix condition.展开更多
This paper is concerned with the nonlinear neutral functional difference equations△x(n) =-a(n)x(n) +h(n)f(n,x(n-T(n)),△x(n-δ(n))),where a,h and f are nonnegative sequences.Sufficient conditions for the existence of...This paper is concerned with the nonlinear neutral functional difference equations△x(n) =-a(n)x(n) +h(n)f(n,x(n-T(n)),△x(n-δ(n))),where a,h and f are nonnegative sequences.Sufficient conditions for the existence of at least three positive T-periodic solutions are established by using a fixed point theorem due to Avery and Peterson.展开更多
By means of an abstract continuation theorem, the existence criteria are established for the positive periodic solutions of a neutral functional differential equation d N d t=N(t)[a(t)-β(t)N(t)-b(t)N(t-σ(t))-c(...By means of an abstract continuation theorem, the existence criteria are established for the positive periodic solutions of a neutral functional differential equation d N d t=N(t)[a(t)-β(t)N(t)-b(t)N(t-σ(t))-c(t)N′(t-τ(t))].展开更多
基金the NSF of Guangxi(2021GXNSFFA196004,GKAD23026237)the NNSF of China(12001478)+4 种基金the China Postdoctoral Science Foundation(2022M721560)the European Union’s Horizon 2020 Research and Innovation Programme under the Marie Sklodowska-Curie grant agreement No.823731 CONMECHthe National Science Center of Poland under Preludium Project(2017/25/N/ST1/00611)the Startup Project of Doctor Scientific Research of Yulin Normal University(G2020ZK07)the Ministry of Science and Higher Education of Republic of Poland(4004/GGPJII/H2020/2018/0,440328/Pn H2/2019)。
文摘In this paper we study a nonstationary Oseen model for a generalized Newtonian incompressible fluid with a time periodic condition and a multivalued,nonmonotone friction law.First,a variational formulation of the model is obtained;that is a nonlinear boundary hemivariational inequality of parabolic type for the velocity field.Then,an abstract first-order evolutionary hemivariational inequality in the framework of an evolution triple of spaces is investigated.Under mild assumptions,the nonemptiness and weak compactness of the set of periodic solutions to the abstract inequality are proven.Furthermore,a uniqueness theorem for the abstract inequality is established by using a monotonicity argument.Finally,we employ the theoretical results to examine the nonstationary Oseen model.
文摘The existence of T_periodic solutions of the nonlinear system with multiple delays is studied. By using the topological degree method, sufficient conditions are obtained for the existence of T_periodic solutions. As an application, the existence of positive periodic solution for a logarithmic population model is established under some conditions.
文摘A periodically homoclinic solution and some rogue wave solutions of (1+1)-dimensional Boussinesq equation are obtained via the limit behavior of parameters and different polynomial functions. Besides, the mathematics reasons for different spatiotemporal structures of rogue waves are analyzed using the extreme value theory of the two-variables function. The diversity of spatiotemporal structures not only depends on the disturbance parameter u0 </sub>but also has a relationship with the other parameters c<sub>0</sub>, α, β.
文摘The existence of positive solutions to second-order periodic BVPs-u"+Mu =j(t, u),t(0) = u(2π),u’(0) = "(2π) and u"+ Mu = I(t, u), u(0) = u(2π), u’(0) = u’(2π)is proved by a simple appliCation of a Fixed point Theorem in cones due to Krasnoselskii.
基金The research supported by the National Natural Science Foundation of China.
文摘This paper deals with the existence of positive periodic solutions for a kind of nonautonomous Volterra intergo-differential equations by employing the Krasnoselskii fixed point theorem. Applying the general theorems established to several biomathematical models, the paper improves some previous results and obtains some new results.
文摘In this paper, the existence of periodic solutions for a time dependent agestructured population model is studied. The averaged net reproductive number is introduced as the main parameter to determine the dynamical behaviors of the model. Theexistence of a globa.l parameterized branch of periodic solutions of the model is obtained byusing the contracting mapping theorem in a periodic and continuous function space. Theglobal stability of the trivial equilibrium is studied and a very practical stability criteriafor the model is obtained. The dynamics of the linear time-periodic model is similar tothat of the linear model.
文摘Considering a decomposition R2N=A⊕B of R2N , we prove in this work, the existence of at least (1+dimA) geometrically distinct periodic solutions for the first-order Hamiltonian system Jx'(t)+H'(t,x(t))+e(t)=0 when the Hamiltonian H(t,u+v) is periodic in (t,u) and its growth at infinity in v is at most like or faster than |v|a, 0≤ae is a forcing term. For the proof, we use the Least Action Principle and a Generalized Saddle Point Theorem.
基金Foundation item: Supported by the Foundation of Education Department of Jiangxi Province(G J J11234) Supported by the Natural Science Foundation of Jiangxi Province(2009GQS0023) Supported by the Natural Science Foundation of Shangrao Normal University(1001)
文摘Based on Mansevich-Mawhin continuation theorem and some analysis skill,some sufficient conditions for the existence of periodic solutions for mixed type p-Laplacian equation with deviating arguments are established,which are complement of previously known results.
文摘The global phase portrait describes the qualitative behaviour of the solution set of a nonlinear ordinary differential equation, for all time. In general, this is as close as we can come to solving nonlinear systems. In this research work we study the dynamics of a bead sliding on a wire with a given specified shape. A long wire is bent into the shape of a curve with equation z = f (x) in a fixed vertical plane. We consider two cases, namely without friction and with friction, specifically for the cubic shape f (x) = x3−x . We derive the corresponding differential equation of motion representing the dynamics of the bead. We then study the resulting second order nonlinear ordinary differential equations, by performing simulations using MathCAD 14. Our main interest is to investigate the existence of periodic solutions for this dynamics in the neighbourhood of the critical points. Our results show clearly that periodic solutions do indeed exist for the frictionless case, as the phase portraits exhibit isolated limit cycles in the phase plane. For the case with friction, the phase portrait depicts a spiral sink, spiraling into the critical point.
文摘For functional difference equations with unbounded delay,we characterized the existence of totally stable and asymptotically almost periodic solution by using stability properties of a bounded solution in a certain limiting equation.
基金Foundation item: Supported by the Anhui Natural Science Foundation(050460103) Supported by the NSF of Anhui Educational Bureau(KJ2008B247) Supported by the RSPYT of Anhui Educational Bu- reau(2008jq1111)
文摘By means of Mawhin's continuation theorem,we study a kind of lie'nard functional differential equations:x"(t)+f(x(t))x'(t)+g(t,x(t-τ(t))) = e(t).Some new results on the existence and uniqueness of periodic solutions are obtained.
基金theNaturalScienceFoundationofEducationalCommitteeofHainanProvince China
文摘By establishing a comparison result and using monotone iterative methods, the theorem of existence for minimal and maximal solutions of periodic boundary value problems for second_order nonlinear integro_differential equations in Banach spaces is proved.
文摘We give sufficient conditions ensuring the existence and uniqueness of an Eberlein-weakly almost periodic solution to the following linear equation dx/dt(t) = A(t)x(t) + f(t) in a Banach space X, where (A(t)) t ∈□ is a family of infinitesimal generators such that for all t ∈□, A(t + T) = A(t) for some T > 0, for which the homogeneuous linear equation dx/dt(t) = A(t)x(t) is well posed, stable and has an exponential dichotomy, and f:□ →X is Eberlein-weakly amost periodic.
基金The project supported by National Natural Science Foundation of China under Grant No. 1007201, the National Key Basic Research Development Project Program under Grant No. G1998030600 and Doctoral Foundation of China under Grant No. 98014119
文摘In this paper, we study the generalized coupled Hirota Satsuma KdV system by using the new generalizedtransformation in homogeneous balance method. As a result, many explicit exact solutions, which contain new solitarywave solutions, periodic wave solutions, and the combined formal solitary wave solutions, and periodic wave solutions,are obtained.
基金supported by the National Natural Science Foundation of China(11371027) the Projects of Outstanding Young Talents of Universities in Anhui Province(gxyq2018116)+2 种基金 the Teaching Groups in Anhui Province(2016jxtd080,2015jxtd048) the NSF of Educational Bureau of Anhui Province(KJ2017A702,KJ2017A704) the NSF of Bozhou University(BZSZKYXM201302,BSKY201539)
文摘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.
文摘In this paper, we consider an almost periodic system which includes a system of the type , where k is a positive integer, aij are almost periodic in n and satisfy aij(n)≥0 for i≠j,? for 1≤j≤m. In the special case where aij(n) are constant functions, above system is a mathematical model of gas dynamics and was treated by T. Carleman and R. D. Jenks for differential systems. In the main theorem, we show that if the m X m matrix (aij(n)) is irreducible, then there exists a positive almost periodic solution which is unique and has some stability. Moreover, we can see that this result gives R. D. Jenks’ result for differential model in the case where aij(n) are constant functions. In Section 3, we consider the linear system with variable cofficients . Even in nonlinear problems, this linear system plays an important role, as their variational equations, and it is requested to determine the uniform asymptotically stability of the zero solution from the information about A(n). In order to obtain the existence of almost periodic solutions of both linear and nonlinear almost periodic discrete systems: above linear system and? for 1≤i≤m, respectively, we shall consider between certain stability properties, which are referred to as uniformly asymptotically stable, and the diagonal dominance matrix condition.
基金Supported by the Natural Science Foundation of Hunan Province(12JJ6006) Supported by the Science Foundation of Department of Science and Technology of Hunan Province(2012FJ3107)
文摘This paper is concerned with the nonlinear neutral functional difference equations△x(n) =-a(n)x(n) +h(n)f(n,x(n-T(n)),△x(n-δ(n))),where a,h and f are nonnegative sequences.Sufficient conditions for the existence of at least three positive T-periodic solutions are established by using a fixed point theorem due to Avery and Peterson.
基金National Natural Science Foundation of China( 198710 0 5 )
文摘By means of an abstract continuation theorem, the existence criteria are established for the positive periodic solutions of a neutral functional differential equation d N d t=N(t)[a(t)-β(t)N(t)-b(t)N(t-σ(t))-c(t)N′(t-τ(t))].