In this paper we investigate the existence of positive solution for a class of fourth_order superlinear semipositone eigenvalue problems. This class of problems usually describes the deformation of the elastic beam wh...In this paper we investigate the existence of positive solution for a class of fourth_order superlinear semipositone eigenvalue problems. This class of problems usually describes the deformation of the elastic beam whose both end_points are fixed.展开更多
The existence of nondecreasing positive solutions for the nonlinear third-order twopoint boundary value problem u′″（t） ＋ q（t）f（t,u（t）,u′（t）） = 0, 0 〈 t 〈 1, u（0） = u″（0） = u′（1） = 0 is studied....The existence of nondecreasing positive solutions for the nonlinear third-order twopoint boundary value problem u′″（t） ＋ q（t）f（t,u（t）,u′（t）） = 0, 0 〈 t 〈 1, u（0） = u″（0） = u′（1） = 0 is studied. The iterative schemes for approximating the solutions are obtained by applying a monotone iterative method.展开更多
The existence of positive solutions and the global attractivity of the difference equation Δy n=r ny nK-y n-l n K-cy n-l n are investigated. And some sufficient conditions are obtained,which greatly imp...The existence of positive solutions and the global attractivity of the difference equation Δy n=r ny nK-y n-l n K-cy n-l n are investigated. And some sufficient conditions are obtained,which greatly improve and extend the known results.展开更多
The existence of positive solutions is investigated for following semipositone nonlinear third-order three-point BVP ω''(t) - λf(t,w(t)) = 0, 0 ≤ t ≤ 1, ω(0) = ω'(n) = ω'(1) = 0.
Abstract The existence of n positive solutions for a class of third-order three-point boundary value problems is investigated, where n is an arbitrary natural number. The main tool is Krasnosel'skii fixed point th...Abstract The existence of n positive solutions for a class of third-order three-point boundary value problems is investigated, where n is an arbitrary natural number. The main tool is Krasnosel'skii fixed point theorem on the cone.展开更多
The existence, multiplicity and uniqueness of positive solutions of a third order two point boundary value problem are discussed with the help of two fixed point theorems in cones, respectively.
Existence and uniqueness conditions for nonnegative solutions to initial value prob- lems of general sublinear-linear differential equations are obtained.They extend the uniqueness theorem due to H.Murakami~[6] and th...Existence and uniqueness conditions for nonnegative solutions to initial value prob- lems of general sublinear-linear differential equations are obtained.They extend the uniqueness theorem due to H.Murakami~[6] and the main results of H.G.Kaper and M.K.Kwong~[4].展开更多
We study the global dynamics of a nonlocal population model with age structure in a bounded domain. We mainly concern with the case where the birth rate decreases as the mature population size become large. The analys...We study the global dynamics of a nonlocal population model with age structure in a bounded domain. We mainly concern with the case where the birth rate decreases as the mature population size become large. The analysis is rather subtle and it is inadequate to apply the powerful theory of monotone dynamical systems. By using the method of super-sub solutions, combined with the careful analysis of the kernel function in the nonlocal term, we prove nonexistence, existence and uniqueness of positive steady states of the model.Moreover, due to the mature individuals do not diffuse, the solution semiflow to the model is not compact. To overcome the difficulty of non-compactness in describing the global asymptotic stability of the unique positive steady state, we first establish an appropriate comparison principle. With the help of the comparison principle,we can employ the theory of dissipative systems to obtain the global asymptotic stability of the unique positive steady state. The main results are illustrated with the nonlocal Nicholson's blowflies equation and the nonlocal Mackey-Glass equation.展开更多
文摘In this paper we investigate the existence of positive solution for a class of fourth_order superlinear semipositone eigenvalue problems. This class of problems usually describes the deformation of the elastic beam whose both end_points are fixed.
基金Supported by the Natural Science Foundation of Zhejiang Province (Y605144)the XNF of Zhejiang University of Media and Communications (XN080012008034)
文摘The existence of nondecreasing positive solutions for the nonlinear third-order twopoint boundary value problem u′″（t） ＋ q（t）f（t,u（t）,u′（t）） = 0, 0 〈 t 〈 1, u（0） = u″（0） = u′（1） = 0 is studied. The iterative schemes for approximating the solutions are obtained by applying a monotone iterative method.
文摘The existence of positive solutions and the global attractivity of the difference equation Δy n=r ny nK-y n-l n K-cy n-l n are investigated. And some sufficient conditions are obtained,which greatly improve and extend the known results.
文摘Abstract The existence of n positive solutions for a class of third-order three-point boundary value problems is investigated, where n is an arbitrary natural number. The main tool is Krasnosel'skii fixed point theorem on the cone.
文摘The existence, multiplicity and uniqueness of positive solutions of a third order two point boundary value problem are discussed with the help of two fixed point theorems in cones, respectively.
文摘Existence and uniqueness conditions for nonnegative solutions to initial value prob- lems of general sublinear-linear differential equations are obtained.They extend the uniqueness theorem due to H.Murakami~[6] and the main results of H.G.Kaper and M.K.Kwong~[4].
基金supported by National Natural Science Foundation of China(Grant Nos.11031002 and 11371107)the Research Fund for the Doctoral Program of Higher Education of China(Grant No.20124410110001)
文摘We study the global dynamics of a nonlocal population model with age structure in a bounded domain. We mainly concern with the case where the birth rate decreases as the mature population size become large. The analysis is rather subtle and it is inadequate to apply the powerful theory of monotone dynamical systems. By using the method of super-sub solutions, combined with the careful analysis of the kernel function in the nonlocal term, we prove nonexistence, existence and uniqueness of positive steady states of the model.Moreover, due to the mature individuals do not diffuse, the solution semiflow to the model is not compact. To overcome the difficulty of non-compactness in describing the global asymptotic stability of the unique positive steady state, we first establish an appropriate comparison principle. With the help of the comparison principle,we can employ the theory of dissipative systems to obtain the global asymptotic stability of the unique positive steady state. The main results are illustrated with the nonlocal Nicholson's blowflies equation and the nonlocal Mackey-Glass equation.
