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, an existence criterion of triple positive solutions to a class of nonlinear beam equations is established using the Leggett-Williams fixed point theorem.An example is also included to demonstrate the re...In this paper, an existence criterion of triple positive solutions to a class of nonlinear beam equations is established using the Leggett-Williams fixed point theorem.An example is also included to demonstrate the result. The interesting point is that the nonlinear term is involved with all low-level derivatives.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
Based on the Guo-Krasnoselskii’s fixed-point theorem,the existence and multiplicity of positive solutions to a boundary value problem(BVP)with two integral boundary conditions{v(4)=f(s,v(s),v′(s),v〞(s)),s∈[0,1],v...Based on the Guo-Krasnoselskii’s fixed-point theorem,the existence and multiplicity of positive solutions to a boundary value problem(BVP)with two integral boundary conditions{v(4)=f(s,v(s),v′(s),v〞(s)),s∈[0,1],v′(1)=v′'′(1)=0,v(0)=∫10 g1(T)v(T )dT ,v′′(0)=∫10 g2( T)v′′(T )d T}are obtained,where f,g1,g2 are all continuous.It generalizes the results of one positive solution to multiplicity and improves some results for integral BVPs.Moreover,some examples are also included to demonstrate our results as applications.展开更多
In this paper, we establish an existence criterion of triple positive solutions of a class of nonlinear fourth-order three-point boundary value problem by the Leggett- Williams fixed point theorem. The interesting poi...In this paper, we establish an existence criterion of triple positive solutions of a class of nonlinear fourth-order three-point boundary value problem by the Leggett- Williams fixed point theorem. The interesting point is that the nonlinear term is involved with all low-level derivatives.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.
基金Supported by the NSF of China(11301241)Institutions of higher learning scientific research project of Gansu Province(2013A-044)+1 种基金Science and Technology Plan Foundation of Gansu Province(145RJYA250)Young Scientists Foundation from Lanzhou Jiaotong University(2011029)
文摘In this paper, an existence criterion of triple positive solutions to a class of nonlinear beam equations is established using the Leggett-Williams fixed point theorem.An example is also included to demonstrate the result. The interesting point is that the nonlinear term is involved with all low-level derivatives.
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.
文摘Based on the Guo-Krasnoselskii’s fixed-point theorem,the existence and multiplicity of positive solutions to a boundary value problem(BVP)with two integral boundary conditions{v(4)=f(s,v(s),v′(s),v〞(s)),s∈[0,1],v′(1)=v′'′(1)=0,v(0)=∫10 g1(T)v(T )dT ,v′′(0)=∫10 g2( T)v′′(T )d T}are obtained,where f,g1,g2 are all continuous.It generalizes the results of one positive solution to multiplicity and improves some results for integral BVPs.Moreover,some examples are also included to demonstrate our results as applications.
基金Supported by the NSF of China(11301241)Science and Technology Plan Foundation of Gansu Province(145RJYA250)+1 种基金Institutions of higher learning scientific research project of Gansu Province(2013A-044)Young Scientist Foundation of Lanzhou Jiaotong University(2011029)
文摘In this paper, we establish an existence criterion of triple positive solutions of a class of nonlinear fourth-order three-point boundary value problem by the Leggett- Williams fixed point theorem. The interesting point is that the nonlinear term is involved with all low-level derivatives.
