scholarly journals Existence of positive solutions for a second order periodic boundary value problem with impulsive effects

2016 ◽  
Vol 43 (1) ◽  
pp. 11 ◽  
Author(s):  
Jiafa Xu ◽  
Zhongli Wei ◽  
Youzheng Ding
Keyword(s):  
Boundary Value Problem ◽  
Positive Solutions ◽  
Periodic Boundary ◽  
Boundary Value ◽  
Second Order ◽  
Impulsive Effects ◽  
Periodic Boundary Value Problem ◽  
Existence Of Positive Solutions

scholarly journals The Existence and Multiplicity of Positive Solutions for Second-Order Periodic Boundary Value Problem

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
Feng Wang ◽  
Fang Zhang ◽  
Fuli Wang
Keyword(s):  
Boundary Value Problem ◽  
Positive Solutions ◽  
Fixed Point Index ◽  
Periodic Boundary ◽  
Boundary Value ◽  
Second Order ◽  
Periodic Boundary Value Problem ◽  
Point Index ◽  
Existence And Multiplicity ◽  
Multiplicity Of Positive Solutions

The existence and multiplicity of positive solutions are established for second-order periodic boundary value problem. Our results are based on the theory of a fixed point index for A-proper semilinear operators defined on cones due to Cremins. Our approach is different in essence from other papers and the main results of this paper are also new.

scholarly journals Existence of Positive Solutions for a Fourth-Order Periodic Boundary Value Problem

2011 ◽  
Vol 2011 ◽  
pp. 1-12
Author(s):  
Yongxiang Li
Keyword(s):  
Boundary Value Problem ◽  
Positive Solutions ◽  
Fourth Order ◽  
Fixed Point Index ◽  
Periodic Boundary ◽  
Boundary Value ◽  
Index Theory ◽  
Periodic Boundary Value Problem ◽  
Fixed Point Index Theory ◽  
Existence Of Positive Solutions

The existence results of positive solutions are obtained for the fourth-order periodic boundary value problemu(4)−βu′′+αu=f(t,u,u′′),0≤t≤1,u(i)(0)=u(i)(1),  i=0,1,2,3, wheref:[0,1]×R+×R→R+is continuous,α,β∈R,and satisfy0<α<((β/2)+2π2)2,β>−2π2,(α/π4)+(β/π2)+1>0. The discussion is based on the fixed point index theory in cones.

scholarly journals The Existence of Positive Solutions for Singular Impulse Periodic Boundary Value Problem

2011 ◽  
Vol 2011 ◽  
pp. 1-12 ◽  
Author(s):  
Zhaocai Hao ◽  
Tanggui Chen
Keyword(s):  
Boundary Value Problem ◽  
Positive Solutions ◽  
Periodic Boundary ◽  
Boundary Value ◽  
Periodic Boundary Value Problem ◽  
Nonlinear Alternative ◽  
Existence Of Positive Solutions ◽  
Alternative Principle

We obtain new result of the existence of positive solutions of a class of singular impulse periodic boundary value problem via a nonlinear alternative principle of Leray-Schauder. We do not require the monotonicity of functions in paper (Zhang and Wang, 2003). An example is also given to illustrate our result.

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