A class of the boundary value problem for fractional order nonlinear differential equation with Riemann-Liouville fractional derivative on the half line was studied. By using the coincidence degree theory due to Mawhi...A class of the boundary value problem for fractional order nonlinear differential equation with Riemann-Liouville fractional derivative on the half line was studied. By using the coincidence degree theory due to Mawhin and constructing the suitable operators,the existence theorem of at least one solution has been established. An example is given to illustrate our result.展开更多
In this paper, we consider existence of single or multiple positive solutions of three-point boundary value problems involving one-dimensional p-Laplacian. We then study existence of solutions when the problems are in...In this paper, we consider existence of single or multiple positive solutions of three-point boundary value problems involving one-dimensional p-Laplacian. We then study existence of solutions when the problems are in resonance cases. The proposed approach is based on the Krasnoselskii＇s fixed point theorem and the coincidence degree.展开更多
By using the continuation theorem of coincidence theory, the existence of a positive periodic solution for a two patches competition system with diffusion and time delay and functional responsex [FK(W1*3/4。*2/3]...By using the continuation theorem of coincidence theory, the existence of a positive periodic solution for a two patches competition system with diffusion and time delay and functional responsex [FK(W1*3/4。*2/3]′ 1 (t)=x 1(t)a 1(t)-b 1(t)x 1(t)-c 1(t)y(t)1+m(t)x 1(t)+D 1(t)[x 2(t)-x 1(t)], x [FK(W1*3/4。*2/3]′ 2 (t)=x 2(t)a 2(t)-b 2(t)x 2(t)-c 2(t)∫ 0 -τ k(s)x 2(t+s) d s+D 2(t)[x 1(t)-x 2(t)], y′(t)=y(t)a 3(t)-b 3(t)y(t)-c 3(t)x 1(t)1+m(t)x 1(t)is established, where a i(t),b i(t),c i(t)(i=1,2,3),m(t) and D i(t)(i=1,2) are all positive periodic continuous functions with period w >0, τ is a nonnegative constant and k(s) is a continuous nonnegative function on [- τ ,0].展开更多
In this paper, a three species diffusive predator-prey model with functional response is studied, where all parameters are time dependent. By using the continuation theorem of coincidence degree theory, the existence ...In this paper, a three species diffusive predator-prey model with functional response is studied, where all parameters are time dependent. By using the continuation theorem of coincidence degree theory, the existence of a positive periodic solution for this system is established.展开更多
The sufficient condition for the existence of2 π- periodic solutions of the following third- order functional differential equations with variable coefficients a(t) x (t) +bx″2 k- 1(t) +cx′2 k- 1(t) + 2 k- 1 i=1...The sufficient condition for the existence of2 π- periodic solutions of the following third- order functional differential equations with variable coefficients a(t) x (t) +bx″2 k- 1(t) +cx′2 k- 1(t) + 2 k- 1 i=1 cixi(t) +g(x(t-τ) ) =p(t) =p(t+2π) is obtained.The approach is based on the abstract continuation theorem from Mawhin and the a- priori estimate of periodic solutions展开更多
A set of easily verifiable sufficient conditions are derived for the existence of positive periodic solutions for delayed generalized predator-prey dispersion systemwhere ai(t),bi(t) and Di(t)(i = 1, 2) axe positive c...A set of easily verifiable sufficient conditions are derived for the existence of positive periodic solutions for delayed generalized predator-prey dispersion systemwhere ai(t),bi(t) and Di(t)(i = 1, 2) axe positive continuous T-periodic functions, gi(t,xi) (i = 1,2) and h(t,y) are continuous and T-periodic with respect to t and h(t,y) > 0 for y>0,t, y∈R,pi(x)(i=1,2) are continuous and monotonously increasing functions, and Pi(xi)>0 for xi>0.展开更多
By means of the continuation theorem of coincidence degree theory, we study a kind of n-order neutral functional differential equation. Some new results on the existence of periodic solutions are obtained.
With the help of the coincidence degree continuation theorem, we generalize to the case of impulsive systems of the second order some existence results obtained by Gaines and Mawhin in the ordinary case. In particular...With the help of the coincidence degree continuation theorem, we generalize to the case of impulsive systems of the second order some existence results obtained by Gaines and Mawhin in the ordinary case. In particular. for the impulsive functions the treatment does not assume any mono- tonicity conditions. which are necessary in earlier papers treated by S.Hu and V.Lakshmikantham, L.H.Erbe and X.Liu with other methods.展开更多
By using the continuation theorem of coincidence degree theory, the existence of a positive periodic solution for a nonautonomous diffusive food chain system of three species.is established, where ri(t), aii(t) (i = 1...By using the continuation theorem of coincidence degree theory, the existence of a positive periodic solution for a nonautonomous diffusive food chain system of three species.is established, where ri(t), aii(t) (i = 1.2,3,4), Di(t) (i = 1,2), a12(t), a21(t), a23(t) and a32(t) are all positive periodic continuous functions with period w > 0, Ti(i = 1,2) are positive constants.展开更多
基金National Natural Science Foundation of China(No.11271248)
文摘A class of the boundary value problem for fractional order nonlinear differential equation with Riemann-Liouville fractional derivative on the half line was studied. By using the coincidence degree theory due to Mawhin and constructing the suitable operators,the existence theorem of at least one solution has been established. An example is given to illustrate our result.
基金Project supported by Foundation of Major Project of ScienceTechnology of Chinese Education Ministy,NSF of Education Committee of Jiangsu Province
文摘In this paper, we consider existence of single or multiple positive solutions of three-point boundary value problems involving one-dimensional p-Laplacian. We then study existence of solutions when the problems are in resonance cases. The proposed approach is based on the Krasnoselskii＇s fixed point theorem and the coincidence degree.
文摘By using the continuation theorem of coincidence theory, the existence of a positive periodic solution for a two patches competition system with diffusion and time delay and functional responsex [FK(W1*3/4。*2/3]′ 1 (t)=x 1(t)a 1(t)-b 1(t)x 1(t)-c 1(t)y(t)1+m(t)x 1(t)+D 1(t)[x 2(t)-x 1(t)], x [FK(W1*3/4。*2/3]′ 2 (t)=x 2(t)a 2(t)-b 2(t)x 2(t)-c 2(t)∫ 0 -τ k(s)x 2(t+s) d s+D 2(t)[x 1(t)-x 2(t)], y′(t)=y(t)a 3(t)-b 3(t)y(t)-c 3(t)x 1(t)1+m(t)x 1(t)is established, where a i(t),b i(t),c i(t)(i=1,2,3),m(t) and D i(t)(i=1,2) are all positive periodic continuous functions with period w >0, τ is a nonnegative constant and k(s) is a continuous nonnegative function on [- τ ,0].
文摘In this paper, a three species diffusive predator-prey model with functional response is studied, where all parameters are time dependent. By using the continuation theorem of coincidence degree theory, the existence of a positive periodic solution for this system is established.
基金Supported by the National Natural Science Foundation of China(1 9971 0 2 6 )
文摘The sufficient condition for the existence of2 π- periodic solutions of the following third- order functional differential equations with variable coefficients a(t) x (t) +bx″2 k- 1(t) +cx′2 k- 1(t) + 2 k- 1 i=1 cixi(t) +g(x(t-τ) ) =p(t) =p(t+2π) is obtained.The approach is based on the abstract continuation theorem from Mawhin and the a- priori estimate of periodic solutions
基金The project is supported by Youth Project Foundation of Hubei Education Department (2002B00002)the Scientific Research Foundation of Hubei Normal University(2003).
文摘A set of easily verifiable sufficient conditions are derived for the existence of positive periodic solutions for delayed generalized predator-prey dispersion systemwhere ai(t),bi(t) and Di(t)(i = 1, 2) axe positive continuous T-periodic functions, gi(t,xi) (i = 1,2) and h(t,y) are continuous and T-periodic with respect to t and h(t,y) > 0 for y>0,t, y∈R,pi(x)(i=1,2) are continuous and monotonously increasing functions, and Pi(xi)>0 for xi>0.
基金supported by the National Natural Science Foundation of China(No10771001)the Key Program of Ministry of Education of China (No205068)the Programof Innovation Team of University of Anhui
文摘By means of the continuation theorem of coincidence degree theory, we study a kind of n-order neutral functional differential equation. Some new results on the existence of periodic solutions are obtained.
文摘With the help of the coincidence degree continuation theorem, we generalize to the case of impulsive systems of the second order some existence results obtained by Gaines and Mawhin in the ordinary case. In particular. for the impulsive functions the treatment does not assume any mono- tonicity conditions. which are necessary in earlier papers treated by S.Hu and V.Lakshmikantham, L.H.Erbe and X.Liu with other methods.
基金Supported by the National Natural Science Foundation of China (No.19971026,10271044).
文摘By using the continuation theorem of coincidence degree theory, the existence of a positive periodic solution for a nonautonomous diffusive food chain system of three species.is established, where ri(t), aii(t) (i = 1.2,3,4), Di(t) (i = 1,2), a12(t), a21(t), a23(t) and a32(t) are all positive periodic continuous functions with period w > 0, Ti(i = 1,2) are positive constants.
