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
The main purpose of this article is to study the existence theories of global meromorphic solutions for some second-order linear differential equations with meromorphic coefficients, which perfect the solution theory ...The main purpose of this article is to study the existence theories of global meromorphic solutions for some second-order linear differential equations with meromorphic coefficients, which perfect the solution theory of such equations.展开更多
This note contains three main results. Firstly, a complete solution of the Linear Non-Homogeneous Matrix Differential Equations (LNHMDEs) is presented that takes into account both the non-zero initial conditions of th...This note contains three main results. Firstly, a complete solution of the Linear Non-Homogeneous Matrix Differential Equations (LNHMDEs) is presented that takes into account both the non-zero initial conditions of the pseudo state and the nonzero initial conditions of the input. Secondly, in order to characterise the dynamics of the LNHMDEs correctly,some important concepts such as the state, slow state (smooth state) and fast state (impulsive state) are generalized to the LNHMDE case and the solution of the LNHMDEs is separated into the smooth (slow) response and the fast (implusive) response. As a third result, a new characterization of the impulsive free initial conditions of the LNHMDEs is given.展开更多
The existence of periodic solutions for a class of impulsive differential equations of mixed type is studied by constructing periodic sequence solutions of difference equations.
In this paper,by using Schaefer fixed-point theorem,the existence of mild solutions of semilinear impulsive delay differential equations with nonlocal conditions is studied.The results obtained are a generalization an...In this paper,by using Schaefer fixed-point theorem,the existence of mild solutions of semilinear impulsive delay differential equations with nonlocal conditions is studied.The results obtained are a generalization and continuation of the recent results on this issue.In the end,an example is given to show the application of the results.展开更多
Oscillation theorems for a second-order impulsive neutral differential equation are established, which extend the main results developed by Li et alLi et al, Oscillation of second order self-coajugate differential equ...Oscillation theorems for a second-order impulsive neutral differential equation are established, which extend the main results developed by Li et alLi et al, Oscillation of second order self-coajugate differential equation with impuls[es. J Comput Appl Math 197（2006）： 78-88] to the considered equation. Two examples are also inserted to illustrate our main results.展开更多
Results on the existence of piecewise continuous solutions for two classes of initial value problems of impulsive singular fractional differential equations are obtained.
In this paper we investigate a class of impulsive differential equations with Dirichlet boundary conditions. Firstly, we define new inner product of <img src="Edit_890fce38-e82b-4f36-be40-9d05e8119b88.png"...In this paper we investigate a class of impulsive differential equations with Dirichlet boundary conditions. Firstly, we define new inner product of <img src="Edit_890fce38-e82b-4f36-be40-9d05e8119b88.png" width="40" height="17" alt="" /> and prove that the norm which is deduced by the inner product is equivalent to the usual norm. Secondly, we construct the lower and upper solutions of (1.1). Thirdly, we obtain the existence of a positive solution, a negative solution and a sign-changing solution by using critical point theory and variational methods. Finally, an example is presented to illustrate the application of our main result.展开更多
In this paper,the existence and uniqueness of iterative solutions to the boundary value problems for a class of first order impulsive integro-differential equations were studied. Under a new concept of upper and lower...In this paper,the existence and uniqueness of iterative solutions to the boundary value problems for a class of first order impulsive integro-differential equations were studied. Under a new concept of upper and lower solutions, a new monotone iterative technique on the boundary value problem of integro-differential equations was proposed. The existence and uniqueness of iterative solutions and the error estimation in certain interval were obtained.An example was also given to illustrate the results.展开更多
Aim To investigate the periodic boundary value problem for functional differential equations with impulses. Methods The method of upper and lower solutions and the monotone iterative technique were used to establish...Aim To investigate the periodic boundary value problem for functional differential equations with impulses. Methods The method of upper and lower solutions and the monotone iterative technique were used to establish our results. Results and Conclusion The results of the existence of maximal and minimal solutions of the periodic boundary value problem for functional differential equations with impulses are obtained.展开更多
Using Nevanlinna theory of the value distribution of meromorphic functions,we discuss some properties of the transcendental meromorphic solutions of second-order algebraic differential equations,and generalize some re...Using Nevanlinna theory of the value distribution of meromorphic functions,we discuss some properties of the transcendental meromorphic solutions of second-order algebraic differential equations,and generalize some results of some authors.展开更多
In this paper, we study the nonlinear second-order boundary value problem of delay differential equation.. Without the assumption of the nonnegativity of f, we still obtain the existence of the positive solution.
In this paper, by using Avery-Peterson theorem on a convex cone, we consider the m-point boundary value problems for second order impulsive differential equations with the nonlinear term depending on the first order d...In this paper, by using Avery-Peterson theorem on a convex cone, we consider the m-point boundary value problems for second order impulsive differential equations with the nonlinear term depending on the first order derivative, the multiplicity result of three positive solutions are obtained.展开更多
A new second-order nonlinear neutral delay differential equation r（t） x（t） ＋ P（t）x（t-τ） ＋ cr（t） x（t）-x（t-τ） ＋ F t,x（t-σ1）,x（t-σ2）,...,x（t-σn） = G（t）,t ≥ t0,where τ 0,σ1,σ2,...,σn ≥ ...A new second-order nonlinear neutral delay differential equation r（t） x（t） ＋ P（t）x（t-τ） ＋ cr（t） x（t）-x（t-τ） ＋ F t,x（t-σ1）,x（t-σ2）,...,x（t-σn） = G（t）,t ≥ t0,where τ 0,σ1,σ2,...,σn ≥ 0,P,r ∈ C（[t0,＋∞）,R）,F ∈ C（[t0,＋∞）×Rn,R）,G ∈ C（[t0,＋∞）,R） and c is a constant,is studied in this paper,and some sufficient conditions for existence of nonoscillatory solutions for this equation are established and expatiated through five theorems according to the range of value of function P（t）.Two examples are presented to illustrate that our works are proper generalizations of the other corresponding results.Furthermore,our results omit the restriction of Q1（t） dominating Q2（t）（See condition C in the text）.展开更多
In this paper, we discuss the existence of positive solutions of the secondorder delay boundary value problems. By applying the fixed-point theorem in a cone, we show the existence of at least one positive solution wi...In this paper, we discuss the existence of positive solutions of the secondorder delay boundary value problems. By applying the fixed-point theorem in a cone, we show the existence of at least one positive solution with singularity and the superlinear semipositone. As an demonstrate our results. application, we also give some examples todemonstrate our results.展开更多
In this paper, by using a fixed point theorem of Krasnoselskii, we study the positive periodic solution for a class of nonlinear periodic differential equation with impulses and delay. Firstly, definition of periodic ...In this paper, by using a fixed point theorem of Krasnoselskii, we study the positive periodic solution for a class of nonlinear periodic differential equation with impulses and delay. Firstly, definition of periodic solution and some lemmas are stated. Then some results of the existence of positive periodic solution about the equation are obtained.展开更多
In this paper, we discuss the maximum and minimum solutions as will as generalized maximum and minimum solutions of nonlinear integrodifferential equations of mixed type with impulses at fixed moments in Banach soaces...In this paper, we discuss the maximum and minimum solutions as will as generalized maximum and minimum solutions of nonlinear integrodifferential equations of mixed type with impulses at fixed moments in Banach soaces by the theorems of fixed points for inreasing operators.展开更多
This paper uses the method of upper and lower solutions and the monotone iterative technique to investigate the existence of maximal and minimal solutions of the periodic boundary value problem for first order impulsi...This paper uses the method of upper and lower solutions and the monotone iterative technique to investigate the existence of maximal and minimal solutions of the periodic boundary value problem for first order impulsive functional differential equations.展开更多
Using the Monch fixed point theorem and progressive estimation method,we study the existence,uniqueness and regularity of mild solutions for damped second order impulsive functional differential equations with infinit...Using the Monch fixed point theorem and progressive estimation method,we study the existence,uniqueness and regularity of mild solutions for damped second order impulsive functional differential equations with infinite delay in Banach spaces.The compactness assumption on associated family of operators and the impulsive term,some restrictive conditions on a priori estimation,noncompactness measure estimation and the impulsive term have not been used,our results are different from some known results.Finally,a noncompact semigroup example explains the obtained results.展开更多
In this paper, we establish a set of sufficient conditions for the controllability of damped second-order impulsive neutral integrodifferential systems with nonlocal initial conditions in Banach spaces. The approach u...In this paper, we establish a set of sufficient conditions for the controllability of damped second-order impulsive neutral integrodifferential systems with nonlocal initial conditions in Banach spaces. The approach used is the Sadovskii fixed point theorem combined with a noncompact condition on the cosine family of operators. An example is oresented to illustrate the result.展开更多
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.
基金Supported by the National Natural Science Foundation of China(11101096 )Guangdong Natural Science Foundation (S2012010010376, S201204006711)
文摘The main purpose of this article is to study the existence theories of global meromorphic solutions for some second-order linear differential equations with meromorphic coefficients, which perfect the solution theory of such equations.
文摘This note contains three main results. Firstly, a complete solution of the Linear Non-Homogeneous Matrix Differential Equations (LNHMDEs) is presented that takes into account both the non-zero initial conditions of the pseudo state and the nonzero initial conditions of the input. Secondly, in order to characterise the dynamics of the LNHMDEs correctly,some important concepts such as the state, slow state (smooth state) and fast state (impulsive state) are generalized to the LNHMDE case and the solution of the LNHMDEs is separated into the smooth (slow) response and the fast (implusive) response. As a third result, a new characterization of the impulsive free initial conditions of the LNHMDEs is given.
基金theAppliedScienceFoundationofYunnan China (97A10 16Q)
文摘The existence of periodic solutions for a class of impulsive differential equations of mixed type is studied by constructing periodic sequence solutions of difference equations.
基金National Natural Science Foundation of China(No.10971139)Fundamental Research Funds for the Central Universities,China(No.B081)
文摘In this paper,by using Schaefer fixed-point theorem,the existence of mild solutions of semilinear impulsive delay differential equations with nonlocal conditions is studied.The results obtained are a generalization and continuation of the recent results on this issue.In the end,an example is given to show the application of the results.
基金Supported by the NSF of Guangdong Province(S2011010004447,S2012040006865)
文摘Oscillation theorems for a second-order impulsive neutral differential equation are established, which extend the main results developed by Li et alLi et al, Oscillation of second order self-coajugate differential equation with impuls[es. J Comput Appl Math 197（2006）： 78-88] to the considered equation. Two examples are also inserted to illustrate our main results.
基金Supported by the Natural Science Foundation of Guangdong Province (S2011010001900)the Guangdong Higher Education Foundation for High-Level Talents
文摘Results on the existence of piecewise continuous solutions for two classes of initial value problems of impulsive singular fractional differential equations are obtained.
文摘In this paper we investigate a class of impulsive differential equations with Dirichlet boundary conditions. Firstly, we define new inner product of <img src="Edit_890fce38-e82b-4f36-be40-9d05e8119b88.png" width="40" height="17" alt="" /> and prove that the norm which is deduced by the inner product is equivalent to the usual norm. Secondly, we construct the lower and upper solutions of (1.1). Thirdly, we obtain the existence of a positive solution, a negative solution and a sign-changing solution by using critical point theory and variational methods. Finally, an example is presented to illustrate the application of our main result.
基金National Natural Science Foundation of China(No.11271372)Hunan Provincial National Natural Science Foundation of China(No.12JJ2004)Central South University Graduate Innovation Project,China(No.2014zzts136)
文摘In this paper,the existence and uniqueness of iterative solutions to the boundary value problems for a class of first order impulsive integro-differential equations were studied. Under a new concept of upper and lower solutions, a new monotone iterative technique on the boundary value problem of integro-differential equations was proposed. The existence and uniqueness of iterative solutions and the error estimation in certain interval were obtained.An example was also given to illustrate the results.
文摘Aim To investigate the periodic boundary value problem for functional differential equations with impulses. Methods The method of upper and lower solutions and the monotone iterative technique were used to establish our results. Results and Conclusion The results of the existence of maximal and minimal solutions of the periodic boundary value problem for functional differential equations with impulses are obtained.
基金Supported by the National Natural Science Foundation of China (Grant No.10471065)the Natural Science Foundation of Guangdong Province (Grant No.04010474)
文摘Using Nevanlinna theory of the value distribution of meromorphic functions,we discuss some properties of the transcendental meromorphic solutions of second-order algebraic differential equations,and generalize some results of some authors.
基金the Youth Research Foundation of Jiangxi University of Finance and Economics(No.04232015)the Technological Project Foundation of Jiangxi Province (Nos.GJJ08358GJJ08359)the Educational Reform Project Foundation of Jiangxi Province (No.JXJG07436)
文摘In this paper, we study the nonlinear second-order boundary value problem of delay differential equation.. Without the assumption of the nonnegativity of f, we still obtain the existence of the positive solution.
基金Supported by the Scientific Research Foundation of Hunan Provincial Education Department(08C826) was also supported by the Aid Program for Science and Technology Innovative Research Team in Higher Educational Institutions of Hunan Province,and the Construct Program of the Key Discipline in Hunan Province.Supported by the National Natural Science Foundation of China(No.i0531050)the innovation group funds (10621101)973 Program of MOST(2006CB805903)
文摘In this paper, by using Avery-Peterson theorem on a convex cone, we consider the m-point boundary value problems for second order impulsive differential equations with the nonlinear term depending on the first order derivative, the multiplicity result of three positive solutions are obtained.
文摘A new second-order nonlinear neutral delay differential equation r（t） x（t） ＋ P（t）x（t-τ） ＋ cr（t） x（t）-x（t-τ） ＋ F t,x（t-σ1）,x（t-σ2）,...,x（t-σn） = G（t）,t ≥ t0,where τ 0,σ1,σ2,...,σn ≥ 0,P,r ∈ C（[t0,＋∞）,R）,F ∈ C（[t0,＋∞）×Rn,R）,G ∈ C（[t0,＋∞）,R） and c is a constant,is studied in this paper,and some sufficient conditions for existence of nonoscillatory solutions for this equation are established and expatiated through five theorems according to the range of value of function P（t）.Two examples are presented to illustrate that our works are proper generalizations of the other corresponding results.Furthermore,our results omit the restriction of Q1（t） dominating Q2（t）（See condition C in the text）.
文摘In this paper, we discuss the existence of positive solutions of the secondorder delay boundary value problems. By applying the fixed-point theorem in a cone, we show the existence of at least one positive solution with singularity and the superlinear semipositone. As an demonstrate our results. application, we also give some examples todemonstrate our results.
基金This research had been supported by the National Nature Science Foundation of China (No. 10241005)the Key Program of Ministry of Education of China (No. 205068).
文摘In this paper, by using a fixed point theorem of Krasnoselskii, we study the positive periodic solution for a class of nonlinear periodic differential equation with impulses and delay. Firstly, definition of periodic solution and some lemmas are stated. Then some results of the existence of positive periodic solution about the equation are obtained.
文摘In this paper, we discuss the maximum and minimum solutions as will as generalized maximum and minimum solutions of nonlinear integrodifferential equations of mixed type with impulses at fixed moments in Banach soaces by the theorems of fixed points for inreasing operators.
文摘This paper uses the method of upper and lower solutions and the monotone iterative technique to investigate the existence of maximal and minimal solutions of the periodic boundary value problem for first order impulsive functional differential equations.
基金Supported in part by the Natural Science Foundation of Anhui Province(11040606M01)Anhui Educational Committee(KJ2012A055),China
文摘Using the Monch fixed point theorem and progressive estimation method,we study the existence,uniqueness and regularity of mild solutions for damped second order impulsive functional differential equations with infinite delay in Banach spaces.The compactness assumption on associated family of operators and the impulsive term,some restrictive conditions on a priori estimation,noncompactness measure estimation and the impulsive term have not been used,our results are different from some known results.Finally,a noncompact semigroup example explains the obtained results.
基金Dr.Arthi was supported by University Grant Commission(UGC),India(No.G2/1287/UGC SAP DRS/2009)
文摘In this paper, we establish a set of sufficient conditions for the controllability of damped second-order impulsive neutral integrodifferential systems with nonlocal initial conditions in Banach spaces. The approach used is the Sadovskii fixed point theorem combined with a noncompact condition on the cosine family of operators. An example is oresented to illustrate the result.
