In this paper we apply fractional calculus to solve the 3rd order ordinary differential equation of the following form: (z-a)(z-b)(z-c)φ 3+(βz 2+γz+D)φ 2+(α(2β-3α-3)z+αγ+α(α+1)(a+b+c))φ 1+α(α-...In this paper we apply fractional calculus to solve the 3rd order ordinary differential equation of the following form: (z-a)(z-b)(z-c)φ 3+(βz 2+γz+D)φ 2+(α(2β-3α-3)z+αγ+α(α+1)(a+b+c))φ 1+α(α-1)(β-2α-2)φ=f.展开更多
In this paper, we investigate the growth of solutions of higher order linear differential equations with meromorphic coefficients. Under certain conditions, we obtain precise estimation of growth order and hyper-order...In this paper, we investigate the growth of solutions of higher order linear differential equations with meromorphic coefficients. Under certain conditions, we obtain precise estimation of growth order and hyper-order of solutions of the equation.展开更多
In this article, the authors study the growth of certain second order linear differential equation f″＋A（z）f′＋B（z）f=0 and give precise estimates for the hyperorder of solutions of infinite order. Under similar ...In this article, the authors study the growth of certain second order linear differential equation f″＋A（z）f′＋B（z）f=0 and give precise estimates for the hyperorder of solutions of infinite order. Under similar conditions, higher order differential equations will be considered.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 article discusses the problems on the existence of meromorphic solutions of some higher order linear differential equations with meromorphic coefficients. Some nice results are obtained. And these results perfect...This article discusses the problems on the existence of meromorphic solutions of some higher order linear differential equations with meromorphic coefficients. Some nice results are obtained. And these results perfect the complex oscillation theory of meromorphic solutions of linear differential equations.展开更多
There are given sufficient conditions for the ultimate boundedness of solutions and for the existence of periodic solutions of a certain vector differential equation of third-order.
This paper is devoted to the study of the linearization problem of system of three second-order ordinary differential equations and . The necessary conditions for linearization by general point transformation and are ...This paper is devoted to the study of the linearization problem of system of three second-order ordinary differential equations and . The necessary conditions for linearization by general point transformation and are found. The sufficient conditions for linearization by restricted class of point transformation and are obtained. Moreover, the procedure for obtaining the linearizing transformation is provided in explicit forms. Examples demonstrating the procedure of using the linearization theorems are presented.展开更多
In this paper we are concerned with the oscillation criteria of second order non-linear homogeneous differential equation. Example have been given to illustrate the results.
By the use of the Liapunov functional approach, a new result is obtained to ascertain the asymptotic stability of zero solution of a certain fourth-order non-linear differential equation with delay. The established re...By the use of the Liapunov functional approach, a new result is obtained to ascertain the asymptotic stability of zero solution of a certain fourth-order non-linear differential equation with delay. The established result is less restrictive than those reported in the literature.展开更多
In this parer, applications of the fractional calculus to the form (Az 2+Bz+C)ψ 2+(Dz+G)ψ 1+Eψ=f and the partial differential equation 2μz 2(Az 2+Bz+C)+(Dz+G)μz+δμ(z,t)=M 2μT 2+NμT, where ψ 1...In this parer, applications of the fractional calculus to the form (Az 2+Bz+C)ψ 2+(Dz+G)ψ 1+Eψ=f and the partial differential equation 2μz 2(Az 2+Bz+C)+(Dz+G)μz+δμ(z,t)=M 2μT 2+NμT, where ψ 1= d ψ d z and ψ 2= d 2ψ d z 2 are presented.展开更多
The Emden differential equation is one of the most widely studied and challenging nonlinear dynamics equations in literature. It finds applications in various areas of study such as celestial mechanics, fluid mechanic...The Emden differential equation is one of the most widely studied and challenging nonlinear dynamics equations in literature. It finds applications in various areas of study such as celestial mechanics, fluid mechanics, Steller structure, isothermal gas spheres, thermionic currents and so on. Because of the importance of the equation, the method of generalized Sundman transformation (GST) as proposed by Nakpim and Meleshko is used for linearizing the Emden differential equation. The Emden differential equation considered here is a modification of the equation given by Berkovic. The results obtained in this paper imply that the Emden equation cannot be linearized by a point transformation. The general solution of the modified Emden equation is also obtained.展开更多
In this paper,we concern ourselves with the existence of positive solutions for a type of integral boundary value problem of fractional differential equations with the fractional order linear derivative operator. By u...In this paper,we concern ourselves with the existence of positive solutions for a type of integral boundary value problem of fractional differential equations with the fractional order linear derivative operator. By using the fixed point theorem in cone,the existence of positive solutions for the boundary value problem is obtained. Some examples are also presented to illustrate the application of our main results.展开更多
In this paper, we investigate the complex oscillation of the higher order differential equation where B0, ...,Bk-1,,F 0 are transcendental meromorpic functions having only finitely many poles. We obtain some precise e...In this paper, we investigate the complex oscillation of the higher order differential equation where B0, ...,Bk-1,,F 0 are transcendental meromorpic functions having only finitely many poles. We obtain some precise estimates of the exponent of convergence of the zero sequence of meromorphic solutions for the above equation.展开更多
In this paper, we investigate the complex oscillation of the non-homogeneous linear differential equation f(k)+Ak-1f(k-1)+… + A0f= F,where among A k-1,…A0, there exists one Ad being an entire function with infinite ...In this paper, we investigate the complex oscillation of the non-homogeneous linear differential equation f(k)+Ak-1f(k-1)+… + A0f= F,where among A k-1,…A0, there exists one Ad being an entire function with infinite order of growth, and the others Aj(j≠d) satisfy m(r,Aj) = 0{m(r,Ad)}, F≠0 is an entire function, and obtain some precise estimates of the exponent of convergence of the zero-sequence of its solutions.展开更多
In this paper we investigate the global asymptotic stability,boundedness as well as the ultimate boundedness of solutions to a general third order nonlinear differential equation,using complete Lyapunov function.
In this paper, we investigate the growth of solutions of a class of higher order linear differential equations with coefficients being gap series. In this case, we remove the condition that the order of coefficients i...In this paper, we investigate the growth of solutions of a class of higher order linear differential equations with coefficients being gap series. In this case, we remove the condition that the order of coefficients in equations is less than 1/2, and obtain some results which improve the previous results.展开更多
In this paper, we investigate complex homogeneous and non-homogeneous higher order linear differential equations with meromorphic coefficients. We obtain several results concerning the iterated order of meromorphic so...In this paper, we investigate complex homogeneous and non-homogeneous higher order linear differential equations with meromorphic coefficients. We obtain several results concerning the iterated order of meromorphic solutions, and the iterated convergence exponent of the zeros of meromorphic solutions.展开更多
文摘In this paper we apply fractional calculus to solve the 3rd order ordinary differential equation of the following form: (z-a)(z-b)(z-c)φ 3+(βz 2+γz+D)φ 2+(α(2β-3α-3)z+αγ+α(α+1)(a+b+c))φ 1+α(α-1)(β-2α-2)φ=f.
文摘In this paper, we investigate the growth of solutions of higher order linear differential equations with meromorphic coefficients. Under certain conditions, we obtain precise estimation of growth order and hyper-order of solutions of the equation.
基金the National Natural Science Foundation of China(10161006,10571044)the Natural Science Foundation of Guangdong Prov(06025059)
文摘In this article, the authors study the growth of certain second order linear differential equation f″＋A（z）f′＋B（z）f=0 and give precise estimates for the hyperorder of solutions of infinite order. Under similar conditions, higher order differential equations will be considered.
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.
基金supported by the National Natural Science Foundation of China (11101096)
文摘This article discusses the problems on the existence of meromorphic solutions of some higher order linear differential equations with meromorphic coefficients. Some nice results are obtained. And these results perfect the complex oscillation theory of meromorphic solutions of linear differential equations.
文摘There are given sufficient conditions for the ultimate boundedness of solutions and for the existence of periodic solutions of a certain vector differential equation of third-order.
文摘This paper is devoted to the study of the linearization problem of system of three second-order ordinary differential equations and . The necessary conditions for linearization by general point transformation and are found. The sufficient conditions for linearization by restricted class of point transformation and are obtained. Moreover, the procedure for obtaining the linearizing transformation is provided in explicit forms. Examples demonstrating the procedure of using the linearization theorems are presented.
文摘In this paper we are concerned with the oscillation criteria of second order non-linear homogeneous differential equation. Example have been given to illustrate the results.
文摘By the use of the Liapunov functional approach, a new result is obtained to ascertain the asymptotic stability of zero solution of a certain fourth-order non-linear differential equation with delay. The established result is less restrictive than those reported in the literature.
文摘In this parer, applications of the fractional calculus to the form (Az 2+Bz+C)ψ 2+(Dz+G)ψ 1+Eψ=f and the partial differential equation 2μz 2(Az 2+Bz+C)+(Dz+G)μz+δμ(z,t)=M 2μT 2+NμT, where ψ 1= d ψ d z and ψ 2= d 2ψ d z 2 are presented.
文摘The Emden differential equation is one of the most widely studied and challenging nonlinear dynamics equations in literature. It finds applications in various areas of study such as celestial mechanics, fluid mechanics, Steller structure, isothermal gas spheres, thermionic currents and so on. Because of the importance of the equation, the method of generalized Sundman transformation (GST) as proposed by Nakpim and Meleshko is used for linearizing the Emden differential equation. The Emden differential equation considered here is a modification of the equation given by Berkovic. The results obtained in this paper imply that the Emden equation cannot be linearized by a point transformation. The general solution of the modified Emden equation is also obtained.
基金supported by Natural Science Foundation of China（No.11171220） Support Projects of University of Shanghai for Science and Technology（No.14XPM01）
文摘In this paper,we concern ourselves with the existence of positive solutions for a type of integral boundary value problem of fractional differential equations with the fractional order linear derivative operator. By using the fixed point theorem in cone,the existence of positive solutions for the boundary value problem is obtained. Some examples are also presented to illustrate the application of our main results.
文摘In this paper, we investigate the complex oscillation of the higher order differential equation where B0, ...,Bk-1,,F 0 are transcendental meromorpic functions having only finitely many poles. We obtain some precise estimates of the exponent of convergence of the zero sequence of meromorphic solutions for the above equation.
文摘In this paper, we investigate the complex oscillation of the non-homogeneous linear differential equation f(k)+Ak-1f(k-1)+… + A0f= F,where among A k-1,…A0, there exists one Ad being an entire function with infinite order of growth, and the others Aj(j≠d) satisfy m(r,Aj) = 0{m(r,Ad)}, F≠0 is an entire function, and obtain some precise estimates of the exponent of convergence of the zero-sequence of its solutions.
文摘In this paper we investigate the global asymptotic stability,boundedness as well as the ultimate boundedness of solutions to a general third order nonlinear differential equation,using complete Lyapunov function.
基金the Youth Foundation of Education Bureau of Jiangxi Province (No. GJJ09463)the Science and Technology Foundation of Education Bureau of Jiangxi Province (No.GJJ08161)
文摘In this paper, we investigate the growth of solutions of a class of higher order linear differential equations with coefficients being gap series. In this case, we remove the condition that the order of coefficients in equations is less than 1/2, and obtain some results which improve the previous results.
基金This work is supported by the National Natural Science Foundation of China (No.10161006)the Natural Science Foundation of Jiangxi Province (No.0311043).
文摘In this paper, we investigate complex homogeneous and non-homogeneous higher order linear differential equations with meromorphic coefficients. We obtain several results concerning the iterated order of meromorphic solutions, and the iterated convergence exponent of the zeros of meromorphic solutions.
