We study the existence of positive solutions of the three-point boundary value problem u＂＋g（t）f（u）=0,t∈（0,1）,u′（0）=0,u（1）=αu（η）, where η∈（0, 1）, and α∈R with 0 〈α〈 1. The existence of posit...We study the existence of positive solutions of the three-point boundary value problem u＂＋g（t）f（u）=0,t∈（0,1）,u′（0）=0,u（1）=αu（η）, where η∈（0, 1）, and α∈R with 0 〈α〈 1. The existence of positive solutions is studied by means of fixed point index theory under some conditions concerning the first eigenvalue with respect to the relevant linear operator. The results, here essentially extend and improve the main result in [1].展开更多
In this paper the existence results of positive ω-periodic solutions are obtained forsecond order ordinary differential equation-u'(t)=f(t,u(t)) (t∈R), and also for firstorder ordinary differential equation u...In this paper the existence results of positive ω-periodic solutions are obtained forsecond order ordinary differential equation-u'(t)=f(t,u(t)) (t∈R), and also for firstorder ordinary differential equation u'(f)=f(t,u(t)) (t∈R), where f: R×R^+→Ris a continuous function which is ω-periodic in t. The discussion is based on the fixedpoint index theory in cones.展开更多
In this paper, the famous Amann three-solution theorem is generalized. Multiplicity question of fixed points for nonlinear operators via two coupled parallel sub-super solutions is studied. Under suitable conditions, ...In this paper, the famous Amann three-solution theorem is generalized. Multiplicity question of fixed points for nonlinear operators via two coupled parallel sub-super solutions is studied. Under suitable conditions, the existence of at least six distinct fixed points of nonlinear operators is proved. The theoretical results are then applied to nonlinear system of Hammerstein integral equations.展开更多
基金the Natural Science Foundation of Gansu Province(3ZS051-A25-016)NWNU-KJCXGCthe Spring-sun program(Z2004-1-62033).
文摘We study the existence of positive solutions of the three-point boundary value problem u＂＋g（t）f（u）=0,t∈（0,1）,u′（0）=0,u（1）=αu（η）, where η∈（0, 1）, and α∈R with 0 〈α〈 1. The existence of positive solutions is studied by means of fixed point index theory under some conditions concerning the first eigenvalue with respect to the relevant linear operator. The results, here essentially extend and improve the main result in [1].
基金Project supported by the National Natural Science Foundation of China (No.10271095), the Gansu Provincial Natural Science Foundation of China (No.ZS031-A25-003-Z) and the NWNU-KJCXGC-212 Foundation
文摘In this paper the existence results of positive ω-periodic solutions are obtained forsecond order ordinary differential equation-u'(t)=f(t,u(t)) (t∈R), and also for firstorder ordinary differential equation u'(f)=f(t,u(t)) (t∈R), where f: R×R^+→Ris a continuous function which is ω-periodic in t. The discussion is based on the fixedpoint index theory in cones.
基金This research is supported by NSFC (10071042)NSFSP (Z2000A02).
文摘In this paper, the famous Amann three-solution theorem is generalized. Multiplicity question of fixed points for nonlinear operators via two coupled parallel sub-super solutions is studied. Under suitable conditions, the existence of at least six distinct fixed points of nonlinear operators is proved. The theoretical results are then applied to nonlinear system of Hammerstein integral equations.
