Sufficient conditions are given to assert that two differentiable mappings between Banach spaces have common values. The proof is essentially based upon continuation methods.
Sufficient conditions were given to assert that between any two Banach spaces over K, Fredholm mappings share at least one .value in a specific open ball. The proof of the result is constructive and based upon continu...Sufficient conditions were given to assert that between any two Banach spaces over K, Fredholm mappings share at least one .value in a specific open ball. The proof of the result is constructive and based upon continuation methods.展开更多
Based on the theory of coincidence degree,the existence of positive periodic solutions is established for a periodic prey predator system with infinite delays (t)=x(t)[α(t)-γ(t)y(t)-γ(t)∫ ∞ 0K 1(t,s)y(t-s) d...Based on the theory of coincidence degree,the existence of positive periodic solutions is established for a periodic prey predator system with infinite delays (t)=x(t)[α(t)-γ(t)y(t)-γ(t)∫ ∞ 0K 1(t,s)y(t-s) d s- ∫ ∞ 0∫ ∞ 0R 1(t,s,θ)y(t-s)y(t-θ) d θ d s], (t)=y(t)[-β(t)+μ(t)x(t)+μ(t)∫ ∞ 0K 2(t,s)x(t-s) d s+ ∫ ∞ 0∫ ∞ 0R 2(t,s,θ)x(t-θ)x(t-s) d θ d s],where α,γ,β,μ are positive continuous ω periodic functions, K i∈C (R×[0,∞),(0,∞))( i =1,2) are ω periodic with respect to their first arguments,.respectively, R i∈C (R×[0,∞)×[0,∞),(0,∞))( i =1,2) are ω periodic with respect to their first arguments,respectively.展开更多
The existence of positive periodic solutions for a periodic Volterra equation with several finite delays and an infinite delay is established. Sufficient conditions for the periodic solutions having global attractivit...The existence of positive periodic solutions for a periodic Volterra equation with several finite delays and an infinite delay is established. Sufficient conditions for the periodic solutions having global attractivity are obtained.展开更多
The existence of a positive periodic solution foru'(t) =u(t)[α(t)-1+β(t)/1+uk(t-τ(t))], t≥0is established. Some sufficient conditions are obtained for the periodic solution to be globally attractive.
A periodic predator-prey system with several delays is studied in this paper. A set of easily verifiable sufficient conditions that guarantee the existence, uniqueness and global attractivity of ...A periodic predator-prey system with several delays is studied in this paper. A set of easily verifiable sufficient conditions that guarantee the existence, uniqueness and global attractivity of the positive periodic solutions is obtained.展开更多
文摘Sufficient conditions are given to assert that two differentiable mappings between Banach spaces have common values. The proof is essentially based upon continuation methods.
基金Project supported by D.G.E.S. Pb 96-1338-CO 2-01 and the Junta de Andalucia
文摘Sufficient conditions were given to assert that between any two Banach spaces over K, Fredholm mappings share at least one .value in a specific open ball. The proof of the result is constructive and based upon continuation methods.
基金This work is partially supported by the Applied Basic Foundation of Yunnan Province of China(9 7A0 1 1 G)
文摘Based on the theory of coincidence degree,the existence of positive periodic solutions is established for a periodic prey predator system with infinite delays (t)=x(t)[α(t)-γ(t)y(t)-γ(t)∫ ∞ 0K 1(t,s)y(t-s) d s- ∫ ∞ 0∫ ∞ 0R 1(t,s,θ)y(t-s)y(t-θ) d θ d s], (t)=y(t)[-β(t)+μ(t)x(t)+μ(t)∫ ∞ 0K 2(t,s)x(t-s) d s+ ∫ ∞ 0∫ ∞ 0R 2(t,s,θ)x(t-θ)x(t-s) d θ d s],where α,γ,β,μ are positive continuous ω periodic functions, K i∈C (R×[0,∞),(0,∞))( i =1,2) are ω periodic with respect to their first arguments,.respectively, R i∈C (R×[0,∞)×[0,∞),(0,∞))( i =1,2) are ω periodic with respect to their first arguments,respectively.
基金This work is supported by the Distinguished Expert Foundation of Naval Aeronautical Engi-neering Academy.
文摘The existence of positive periodic solutions for a periodic Volterra equation with several finite delays and an infinite delay is established. Sufficient conditions for the periodic solutions having global attractivity are obtained.
基金This work is supported by Science Foundation of Hunan Provincial Education Cominission.
文摘The existence of a positive periodic solution foru'(t) =u(t)[α(t)-1+β(t)/1+uk(t-τ(t))], t≥0is established. Some sufficient conditions are obtained for the periodic solution to be globally attractive.
基金This work is supported by the Distinguished Expert Foundation of Naval Aeronautical Engineering Institute.
文摘A periodic predator-prey system with several delays is studied in this paper. A set of easily verifiable sufficient conditions that guarantee the existence, uniqueness and global attractivity of the positive periodic solutions is obtained.
