This article is concerned with a population dynamic model with delay and quiescent stage. By using the weighted-energy method combining continuation method, the exponential stability of traveling waves of the model un...This article is concerned with a population dynamic model with delay and quiescent stage. By using the weighted-energy method combining continuation method, the exponential stability of traveling waves of the model under non-quasi-monotonicity conditions is established. Particularly, the requirement for initial perturbation is weaker and it is uniformly bounded only at x = ＋∞ but may not be vanishing.展开更多
By using the weighted-energy method combining continuation method, the exponential stability of monostable traveling waves for a delayed equation without quasimonotonicity is established, including even the slower wav...By using the weighted-energy method combining continuation method, the exponential stability of monostable traveling waves for a delayed equation without quasimonotonicity is established, including even the slower waves whose speed are close to the critical speed. Particularly, the nonlinearity is nonlocal in the equation and the initial perturbation is uniformly bounded only at x=+∞ but may not be vanishing.展开更多
In this paper,the existence and multiplicity of positive solutions for a class of non-resonant fourth-order integral boundary value problem{u(4)(t)+βu″(t)-au(t)=f(t,u(t),u″(t)),t∈(0,1),u″(0)=u″(1)=0,u(0)=0,u(1)=...In this paper,the existence and multiplicity of positive solutions for a class of non-resonant fourth-order integral boundary value problem{u(4)(t)+βu″(t)-au(t)=f(t,u(t),u″(t)),t∈(0,1),u″(0)=u″(1)=0,u(0)=0,u(1)=(1/λ2-1/λ1)∫01q(s)f(s,u(s),u″(s))ds with two parameters are established by using the Guo-Krasnoselskii's fixedpoint theorem,where f∈C([0,1]×[0,+∞)×(-∞,0],[0,+∞)),q(t)∈L1[0,1]is nonnegative,α,β∈R and satisfyβ<2π2,α>0,α/π4+β/π2<1,λ1,2=(-β+√β^2+4a)/2.The corresponding examples are raised to demonstrate the results we obtained.展开更多
基金supported by the NSF of China(11761046,11301241)
文摘This article is concerned with a population dynamic model with delay and quiescent stage. By using the weighted-energy method combining continuation method, the exponential stability of traveling waves of the model under non-quasi-monotonicity conditions is established. Particularly, the requirement for initial perturbation is weaker and it is uniformly bounded only at x = ＋∞ but may not be vanishing.
文摘By using the weighted-energy method combining continuation method, the exponential stability of monostable traveling waves for a delayed equation without quasimonotonicity is established, including even the slower waves whose speed are close to the critical speed. Particularly, the nonlinearity is nonlocal in the equation and the initial perturbation is uniformly bounded only at x=+∞ but may not be vanishing.
文摘In this paper,the existence and multiplicity of positive solutions for a class of non-resonant fourth-order integral boundary value problem{u(4)(t)+βu″(t)-au(t)=f(t,u(t),u″(t)),t∈(0,1),u″(0)=u″(1)=0,u(0)=0,u(1)=(1/λ2-1/λ1)∫01q(s)f(s,u(s),u″(s))ds with two parameters are established by using the Guo-Krasnoselskii's fixedpoint theorem,where f∈C([0,1]×[0,+∞)×(-∞,0],[0,+∞)),q(t)∈L1[0,1]is nonnegative,α,β∈R and satisfyβ<2π2,α>0,α/π4+β/π2<1,λ1,2=(-β+√β^2+4a)/2.The corresponding examples are raised to demonstrate the results we obtained.
