Existence of positive solutions for periodic boundary value problem with sign-changing Green’s function

Positivity ◽  
2018 ◽  
Vol 22 (5) ◽  
pp. 1269-1279 ◽  
Author(s):  
D. D. Hai
Keyword(s):  
Boundary Value Problem ◽  
Green’S Function ◽  
Positive Solutions ◽  
Green's Function ◽  
Periodic Boundary ◽  
Boundary Value ◽  
Periodic Boundary Value Problem ◽  
Existence Of Positive Solutions

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 Positive Solutions for a Fractional Boundary Value Problem with a Perturbation Term

2018 ◽  
Vol 2018 ◽  
pp. 1-5 ◽  
Author(s):  
Yumei Zou
Keyword(s):  
Boundary Value Problem ◽  
Green’S Function ◽  
Positive Solutions ◽  
Green's Function ◽  
Boundary Value ◽  
Fractional Boundary Value Problem ◽  
Perturbation Term ◽  
Existence Of Positive Solutions

We obtain some new upper and lower estimates for the Green’s function associated with a fractional boundary value problem with a perturbation term. Criteria for the existence of positive solutions of the problem are then obtained based on it.

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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