scholarly journals Positive Solutions for Neumann Boundary Value Problems of Second-Order Impulsive Differential Equations in Banach Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Xiaoya Liu ◽  
Yongxiang Li
Keyword(s):  
Differential Equations ◽  
Positive Solutions ◽  
Boundary Value ◽  
Impulsive Differential Equations ◽  
Neumann Boundary ◽  
Index Theory ◽  
Second Order ◽  
Positive Elements ◽  
Fixed Point Index Theory ◽  
Neumann Boundary Value Problems

The existence of positive solutions for Neumann boundary value problem of second-order impulsive differential equations−u″(t)+Mu(t)=f(t,u(t),t∈J,t≠tk,-Δu'|t=tk=Ik(u(tk)),k=1,2,…,m,u'(0)=u'(1)=θ, in an ordered Banach spaceEwas discussed by employing the fixed point index theory of condensing mapping, whereM>0is a constant,J=[0,1],f∈C(J×K,K),Ik∈C(K,K),k=1,2,…,m, andKis the cone of positive elements inE. Moreover, an application is given to illustrate the main result.

scholarly journals Positive solutions of a discrete second-order boundary value problems with fully nonlinear term

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Liyun Jin ◽  
Hua Luo
Keyword(s):  
Positive Solutions ◽  
Fixed Point Index ◽  
Nonlinear Term ◽  
Boundary Value ◽  
Index Theory ◽  
Second Order ◽  
Fully Nonlinear ◽  
Fixed Point Index Theory ◽  
Weaker Conditions ◽  
Lower Limits

Abstract In this paper, we mainly consider a kind of discrete second-order boundary value problem with fully nonlinear term. By using the fixed-point index theory, we obtain some existence results of positive solutions of this kind of problems. Instead of the upper and lower limits condition on f, we may only impose some weaker conditions on f.

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