This paper deals with the singular perturbation of the boundary value problem of the systems for quasi-linear ordinary differential equationswhere x,f, y , h, A, B and C all belong to Rn , and g is an n×n matrix ...This paper deals with the singular perturbation of the boundary value problem of the systems for quasi-linear ordinary differential equationswhere x,f, y , h, A, B and C all belong to Rn , and g is an n×n matrix function. Under suitable conditions we prove the existence of the solutions by diagonalization and the fixed point theorem and also estimate the remainder.展开更多
First, an asynchronous distributed parallel evolutionary modeling algorithm (PEMA) for building the model of system of ordinary differential equations for dynamical systems is proposed in this paper. Then a series of ...First, an asynchronous distributed parallel evolutionary modeling algorithm (PEMA) for building the model of system of ordinary differential equations for dynamical systems is proposed in this paper. Then a series of parallel experiments have been conducted to systematically test the influence of some important parallel control parameters on the performance of the algorithm. A lot of experimental results are obtained and we make some analysis and explanations to them.展开更多
This article considers the Dirichlet problem of homogeneous and inhomogeneous second-order ordinary differential systems. A nondegeneracy result is proven for positive solutions of homogeneous systems. Sufficient and ...This article considers the Dirichlet problem of homogeneous and inhomogeneous second-order ordinary differential systems. A nondegeneracy result is proven for positive solutions of homogeneous systems. Sufficient and necessary conditions for the existence of multiple positive solutions for inhomogeneous systems are obtained by making use of the nondegeneracy and uniqueness results of homogeneous systems.展开更多
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 article we proposed a method for constructing approximations to periodic solutions of one class nonautonomous system of ordinary differential equations. It is based on successive approximation scheme using par...In this article we proposed a method for constructing approximations to periodic solutions of one class nonautonomous system of ordinary differential equations. It is based on successive approximation scheme using parallel symbolic calculations to obtain solutions in analytical form. We showed the convergence of the scheme of successive approximations on the period, and also considered an example of a second order system where the described scheme of calculations can be applied.展开更多
The multisplitting algorithm for solving large systems of ordinary differential equations on parallel computers was introduced by Jeltsch and Pohl in [1]. On fixed time intervals conver gence results could be derived ...The multisplitting algorithm for solving large systems of ordinary differential equations on parallel computers was introduced by Jeltsch and Pohl in [1]. On fixed time intervals conver gence results could be derived if the subsystems are solving exactly.Firstly,in theis paper,we deal with an extension of the waveform relaxation algorithm by us ing multisplittin AOR method based on an overlapping block decomposition. We restricted our selves to equidistant timepoints and dealed with the case that an implicit integration method was used to solve the subsystems numerically in parallel. Then we have proved convergence of multi splitting AOR waveform relaxation algorithm on a fixed window containing a finite number of timepoints.展开更多
In this paper, we establish a result of Leray-Schauder degree on the order interval which is induced by a pair of strict lower and upper solutions for a system of second-order ordinary differential equations. As appli...In this paper, we establish a result of Leray-Schauder degree on the order interval which is induced by a pair of strict lower and upper solutions for a system of second-order ordinary differential equations. As applications, we prove the global existence of positive solutions for a multi-parameter system of second-order ordinary differential equations with respect to parameters. The discussion is based on the result of Leray- Schauder degree on the order interval and the fixed point index theory in cones.展开更多
By using topological method, we study a class of boundary value problem for a system of nonlinear ordinary differential equations. Under suitable conditions, we prove the existence of positive solution of the problem.
In this paper, we establish the product formula for the fixed point index on product cone, andthen, as applications, consider the existence, nonexistence and multiplicity of positive solutions for a second-order ordin...In this paper, we establish the product formula for the fixed point index on product cone, andthen, as applications, consider the existence, nonexistence and multiplicity of positive solutions for a second-order ordinary differential system with parameters. The discussion is based on the product formula and thefundamental properties of the fixed point index.展开更多
In this paper, a theorem of the local qualitative classification of equllibrium of a special type of higher order ordinary differential system is provided for establishing the theoretical bases to extend the planer. ...In this paper, a theorem of the local qualitative classification of equllibrium of a special type of higher order ordinary differential system is provided for establishing the theoretical bases to extend the planer. qualitative nomgraphy in [1] to the special geometricaljy qualitative method in 3-dimensions.展开更多
In this paper,we consider an asymptotically linear second-order ordinary differential system with Dirchlet boundary value conditions. Under some conditions,we show the multiplicity of solutions to the system by the Mo...In this paper,we consider an asymptotically linear second-order ordinary differential system with Dirchlet boundary value conditions. Under some conditions,we show the multiplicity of solutions to the system by the Morse theory and an index theory.展开更多
This work seeks to describe intra-solution particle movement system. It makes use of data obtained from simulations of patients on efavirenz. A system of ordinary differential equations is used to model movement state...This work seeks to describe intra-solution particle movement system. It makes use of data obtained from simulations of patients on efavirenz. A system of ordinary differential equations is used to model movement state at some particular concentration. The movement states’ description is found for the primary and secondary level. The primary system is found to be predominantly an unstable system while the secondary system is stable. This is derived from the state of dynamic eigenvalues associated with the system. The saturated solution-particle is projected to be stable both for the primary potential and secondary state. A volume conserving linear system has been suggested to describe the dynamical state of movement of a solution particle.展开更多
This paper is concerned with the existence of periodic solutions for a nonlinear system of ordinary differential equations.We obtain a Nagumo-type a priori bound for the periodic solutions and then by using this a pri...This paper is concerned with the existence of periodic solutions for a nonlinear system of ordinary differential equations.We obtain a Nagumo-type a priori bound for the periodic solutions and then by using this a priori bound we prove the existence of at least one T-periodic solution under some general conditions展开更多
文摘This paper deals with the singular perturbation of the boundary value problem of the systems for quasi-linear ordinary differential equationswhere x,f, y , h, A, B and C all belong to Rn , and g is an n×n matrix function. Under suitable conditions we prove the existence of the solutions by diagonalization and the fixed point theorem and also estimate the remainder.
基金Supported by the National Natural Science Foundation of China(60133010,70071042,60073043)
文摘First, an asynchronous distributed parallel evolutionary modeling algorithm (PEMA) for building the model of system of ordinary differential equations for dynamical systems is proposed in this paper. Then a series of parallel experiments have been conducted to systematically test the influence of some important parallel control parameters on the performance of the algorithm. A lot of experimental results are obtained and we make some analysis and explanations to them.
基金supported by the NNSF of China(10671064)the second author was supported by the Australian Research Council's Discovery Projects(DP0450752)
文摘This article considers the Dirichlet problem of homogeneous and inhomogeneous second-order ordinary differential systems. A nondegeneracy result is proven for positive solutions of homogeneous systems. Sufficient and necessary conditions for the existence of multiple positive solutions for inhomogeneous systems are obtained by making use of the nondegeneracy and uniqueness results of homogeneous systems.
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 article we proposed a method for constructing approximations to periodic solutions of one class nonautonomous system of ordinary differential equations. It is based on successive approximation scheme using parallel symbolic calculations to obtain solutions in analytical form. We showed the convergence of the scheme of successive approximations on the period, and also considered an example of a second order system where the described scheme of calculations can be applied.
文摘The multisplitting algorithm for solving large systems of ordinary differential equations on parallel computers was introduced by Jeltsch and Pohl in [1]. On fixed time intervals conver gence results could be derived if the subsystems are solving exactly.Firstly,in theis paper,we deal with an extension of the waveform relaxation algorithm by us ing multisplittin AOR method based on an overlapping block decomposition. We restricted our selves to equidistant timepoints and dealed with the case that an implicit integration method was used to solve the subsystems numerically in parallel. Then we have proved convergence of multi splitting AOR waveform relaxation algorithm on a fixed window containing a finite number of timepoints.
基金Supported in part by the National Natural Science Foundation (No.11101404) of Chinathe Fundamental Research Funds for the Central Universities (No.lzujbky-2012-11)
文摘In this paper, we establish a result of Leray-Schauder degree on the order interval which is induced by a pair of strict lower and upper solutions for a system of second-order ordinary differential equations. As applications, we prove the global existence of positive solutions for a multi-parameter system of second-order ordinary differential equations with respect to parameters. The discussion is based on the result of Leray- Schauder degree on the order interval and the fixed point index theory in cones.
基金The Project Supported by the National Natural Science Foundation of China (10371066).
文摘By using topological method, we study a class of boundary value problem for a system of nonlinear ordinary differential equations. Under suitable conditions, we prove the existence of positive solution of the problem.
基金supported by Natural Science Foundation in Jiangsu Province (Grant Nos.10KJB110004, 08KJD110010)National Natural Science Foundation of China (Grant Nos. 10971046, 10831005, 10671195)China Postdoctoral Science Foundation (Grant Nos. 20090450601)
文摘In this paper, we establish the product formula for the fixed point index on product cone, andthen, as applications, consider the existence, nonexistence and multiplicity of positive solutions for a second-order ordinary differential system with parameters. The discussion is based on the product formula and thefundamental properties of the fixed point index.
文摘In this paper, a theorem of the local qualitative classification of equllibrium of a special type of higher order ordinary differential system is provided for establishing the theoretical bases to extend the planer. qualitative nomgraphy in [1] to the special geometricaljy qualitative method in 3-dimensions.
文摘In this paper,we consider an asymptotically linear second-order ordinary differential system with Dirchlet boundary value conditions. Under some conditions,we show the multiplicity of solutions to the system by the Morse theory and an index theory.
文摘This work seeks to describe intra-solution particle movement system. It makes use of data obtained from simulations of patients on efavirenz. A system of ordinary differential equations is used to model movement state at some particular concentration. The movement states’ description is found for the primary and secondary level. The primary system is found to be predominantly an unstable system while the secondary system is stable. This is derived from the state of dynamic eigenvalues associated with the system. The saturated solution-particle is projected to be stable both for the primary potential and secondary state. A volume conserving linear system has been suggested to describe the dynamical state of movement of a solution particle.
基金Research supported by the NNSF of China and the RFDP of China.
文摘This paper is concerned with the existence of periodic solutions for a nonlinear system of ordinary differential equations.We obtain a Nagumo-type a priori bound for the periodic solutions and then by using this a priori bound we prove the existence of at least one T-periodic solution under some general conditions
