The investigations on Ge-implanted GaN films grown by MOCVD and then annealed at 1100℃ under ammonia ambient have been carried out. With increasing Ge implantation dose, four additional peaks arise at wave numbers of...The investigations on Ge-implanted GaN films grown by MOCVD and then annealed at 1100℃ under ammonia ambient have been carried out. With increasing Ge implantation dose, four additional peaks arise at wave numbers of 260, 314, 428 and 670cm -1 in Ramam spectra. In PL spectra, the relative intensity of the band-edge emission compared to the PL-band centered at 2.66eV and the yellow band decreases with increase of Ge-implanted dose. The modes of 260 and 314cm -1 are attributed to disorder-activated Raman scattering, whereas the modes of 428 and 670cm -1 are assigned to local vibrations of vacancies and vacancy-related complexes. The PL-band centered at 2.66eV and the yellow band is also related to these vacancy defects. The new Raman peak at 301cm -1 for the sample annealed only 5min originates from Ge clusters due to deficient annealing.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
Some sufficient conditions for the oscillation of all solutions of the delay differential equations with positive and negative coefficientsare obtained, where 0 < αi, βi <1,pi>, qi >, are constants, t = ...Some sufficient conditions for the oscillation of all solutions of the delay differential equations with positive and negative coefficientsare obtained, where 0 < αi, βi <1,pi>, qi >, are constants, t = 1,2, …, n.展开更多
In this paper, by making use of the integral method and some results of the functional differential equations, oscillatory properties of the solutions of certain parabolic partial differential equations with multi-del...In this paper, by making use of the integral method and some results of the functional differential equations, oscillatory properties of the solutions of certain parabolic partial differential equations with multi-delays are investigated and a series of necessary and sufficient conditions for oscillations of the equations are established. The results fully indicate that the oscillations are caused by the delay and hence reveal the varied difference between these equations and those without delay.展开更多
In this paper, we consider the existence of positive solutions of the semlinear elliptic boundary value problem with convex and concave nonlinearities, the results obtained improve and generalize some known results.
This paper, deals with the oscillatory properties of a class of hyperbolic functional differential equations and obtains a set of criterions, by using some results of functional differential inequality. These results ...This paper, deals with the oscillatory properties of a class of hyperbolic functional differential equations and obtains a set of criterions, by using some results of functional differential inequality. These results reveal that the varied difference between hyperbolic functional differential equations and hyperbolic differential equations.展开更多
In this paper, by means of iterative analysis, the existence for periodic boundary value problem of first-order integro-differential differential equations are considered. Some new results are obtained.
In this paper, oscillatory properties for solutions of certain nonlinear impulsive parabolic equation are investigated and a series of new sufficient conditions is established.
In this paper, we give complete qualitative analysis on a class of biological system and prove the nonexistence, existence and uniqueness of a limit cycle for the system.
In this paper, we study the singular perturbation of boundary value problem for a class of n-th order nonlinear differential equation, the solution is shown to exhibit multiple layer behavior. According to different l...In this paper, we study the singular perturbation of boundary value problem for a class of n-th order nonlinear differential equation, the solution is shown to exhibit multiple layer behavior. According to different layers and by introducing extended variable, we obtain the uniformly effective asymptotic expansion with different boundary layer correction term.展开更多
In this paper, we study some permanence and global stability to a nonautonomous nonlinear discrete single species system, and obtain some sufficient condition of global stability to the system.
基金Natural Science Foundation from Huaihai Institute of Technology(Z2004031)
文摘The investigations on Ge-implanted GaN films grown by MOCVD and then annealed at 1100℃ under ammonia ambient have been carried out. With increasing Ge implantation dose, four additional peaks arise at wave numbers of 260, 314, 428 and 670cm -1 in Ramam spectra. In PL spectra, the relative intensity of the band-edge emission compared to the PL-band centered at 2.66eV and the yellow band decreases with increase of Ge-implanted dose. The modes of 260 and 314cm -1 are attributed to disorder-activated Raman scattering, whereas the modes of 428 and 670cm -1 are assigned to local vibrations of vacancies and vacancy-related complexes. The PL-band centered at 2.66eV and the yellow band is also related to these vacancy defects. The new Raman peak at 301cm -1 for the sample annealed only 5min originates from Ge clusters due to deficient annealing.
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.
基金Project supported by Scientific Research Fund of Hunan Provincial Education Department (China)(granted 03C427).
文摘Some sufficient conditions for the oscillation of all solutions of the delay differential equations with positive and negative coefficientsare obtained, where 0 < αi, βi <1,pi>, qi >, are constants, t = 1,2, …, n.
文摘In this paper, by making use of the integral method and some results of the functional differential equations, oscillatory properties of the solutions of certain parabolic partial differential equations with multi-delays are investigated and a series of necessary and sufficient conditions for oscillations of the equations are established. The results fully indicate that the oscillations are caused by the delay and hence reveal the varied difference between these equations and those without delay.
文摘In this paper, we consider the existence of positive solutions of the semlinear elliptic boundary value problem with convex and concave nonlinearities, the results obtained improve and generalize some known results.
基金This work is supported by the Natural Science Foundation of Hubei Province.
文摘This paper, deals with the oscillatory properties of a class of hyperbolic functional differential equations and obtains a set of criterions, by using some results of functional differential inequality. These results reveal that the varied difference between hyperbolic functional differential equations and hyperbolic differential equations.
基金National Natural Science Foundation of China (No.50579089)Natural Science Foundation of Hubei Provincial Department of Education (No.B200704001)+1 种基金Science Foundation for Young of China University of Geosciences (No.CUGQNL0615)Science Foundation for Graduate of China University of Geosciences (No.CUGYJS0709)
文摘In this paper, by means of iterative analysis, the existence for periodic boundary value problem of first-order integro-differential differential equations are considered. Some new results are obtained.
基金This work is supported by National Natural Science Foundation of China (40373003 and 40372121) and by CUGQNL0517.
文摘In this paper, oscillatory properties for solutions of certain nonlinear impulsive parabolic equation are investigated and a series of new sufficient conditions is established.
文摘In this paper, we give complete qualitative analysis on a class of biological system and prove the nonexistence, existence and uniqueness of a limit cycle for the system.
基金Supported by Natural Sci.Fund of Anhui Education Office under contract No.KJ2007A013.
文摘In this paper, we study the singular perturbation of boundary value problem for a class of n-th order nonlinear differential equation, the solution is shown to exhibit multiple layer behavior. According to different layers and by introducing extended variable, we obtain the uniformly effective asymptotic expansion with different boundary layer correction term.
基金the Natural Sciences Foundation of Fujian Province (Z0511044).
文摘In this paper, we study some permanence and global stability to a nonautonomous nonlinear discrete single species system, and obtain some sufficient condition of global stability to the system.
