By the generalized Riccati transformation and the integral averaging technique, some sufficient conditions of oscillation of the solutions for second order nonlinear differential equations with damping were discussed....By the generalized Riccati transformation and the integral averaging technique, some sufficient conditions of oscillation of the solutions for second order nonlinear differential equations with damping were discussed.Some sufficient oscillation criteria for previous equations were built up.Some oscillation criteria have been expanded and strengthened in some other known results.展开更多
Some new oscillation theorems are established for the second order nonlinear differential equations with damping of the form where p（t） and q（t） are allowed to change sign on [t0,∞).
In this paper existence, uniqueness and asymptotic estimations of solutions of the boundary value problems on infinite interval for the second order nonlinear equation depending singularly on a small parameterare exam...In this paper existence, uniqueness and asymptotic estimations of solutions of the boundary value problems on infinite interval for the second order nonlinear equation depending singularly on a small parameterare examined, where are constants, and i=0,1.展开更多
In this paper,we study the existence of quasi-periodic solutions and the bound- edness of solutions for a wide class nonlinear differential equations of second order.Using the KAM theorem of reversible systems and the...In this paper,we study the existence of quasi-periodic solutions and the bound- edness of solutions for a wide class nonlinear differential equations of second order.Using the KAM theorem of reversible systems and the theory of transformations,we obtain the existence of quasi-periodic solutions and the boundedness of solutions under some reasonable conditions.展开更多
In this paper, we present and analyze a single interval Legendre-Gaussspectral collocation method for solving the second order nonlinear delay differentialequations with variable delays. We also propose a novel algori...In this paper, we present and analyze a single interval Legendre-Gaussspectral collocation method for solving the second order nonlinear delay differentialequations with variable delays. We also propose a novel algorithm for the singleinterval scheme and apply it to the multiple interval scheme for more efficient implementation. Numerical examples are provided to illustrate the high accuracy ofthe proposed methods.展开更多
An existence-uniqueness result is given for second order nonlinear differential equations with Robin boundary conditionwhere αi, βi,(i =1,2), α and b are all constants.And the resonant points of this problemare als...An existence-uniqueness result is given for second order nonlinear differential equations with Robin boundary conditionwhere αi, βi,(i =1,2), α and b are all constants.And the resonant points of this problemare also evaluated.AMS(MOS) Subject classifications 34B15展开更多
文摘By the generalized Riccati transformation and the integral averaging technique, some sufficient conditions of oscillation of the solutions for second order nonlinear differential equations with damping were discussed.Some sufficient oscillation criteria for previous equations were built up.Some oscillation criteria have been expanded and strengthened in some other known results.
文摘Some new oscillation theorems are established for the second order nonlinear differential equations with damping of the form where p（t） and q（t） are allowed to change sign on [t0,∞).
文摘In this paper existence, uniqueness and asymptotic estimations of solutions of the boundary value problems on infinite interval for the second order nonlinear equation depending singularly on a small parameterare examined, where are constants, and i=0,1.
文摘In this paper,we study the existence of quasi-periodic solutions and the bound- edness of solutions for a wide class nonlinear differential equations of second order.Using the KAM theorem of reversible systems and the theory of transformations,we obtain the existence of quasi-periodic solutions and the boundedness of solutions under some reasonable conditions.
基金The first author is supported in part by the National Science Foundation of China(Nos.11226330 and 11301343)the Research Fund for the Doctoral Program of Higher Education of China(No.20113127120002)+5 种基金the Research Fund for Young Teachers Program in Shanghai(No.shsf018)and the Fund for E-institute of Shanghai Universities(No.E03004)The second author is supported in part by the National Science Foundation of China(No.11171225)the Research Fund for the Doctoral Program of Higher Education of China(No.20133127110006)the Innovation Program of Shanghai Municipal Education Commission(No.12ZZ131)the Fund for E-institute of Shanghai Universities(No.E03004).
文摘In this paper, we present and analyze a single interval Legendre-Gaussspectral collocation method for solving the second order nonlinear delay differentialequations with variable delays. We also propose a novel algorithm for the singleinterval scheme and apply it to the multiple interval scheme for more efficient implementation. Numerical examples are provided to illustrate the high accuracy ofthe proposed methods.
文摘An existence-uniqueness result is given for second order nonlinear differential equations with Robin boundary conditionwhere αi, βi,(i =1,2), α and b are all constants.And the resonant points of this problemare also evaluated.AMS(MOS) Subject classifications 34B15
