Multiple symmetric positive solutions of fourth-order two point boundary value problem

2006 ◽  
Vol 22 (1-2) ◽  
pp. 295-306 ◽  
Author(s):  
De-Xiang Ma ◽  
Wei-Gao Ge
Keyword(s):  
Boundary Value Problem ◽  
Positive Solutions ◽  
Fourth Order ◽  
Boundary Value ◽  
Point Boundary ◽  
Symmetric Positive Solutions

scholarly journals Monotone Iterative Technique and Symmetric Positive Solutions to Fourth-Order Boundary Value Problem with Integral Boundary Conditions

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Huihui Pang ◽  
Chen Cai
Keyword(s):  
Boundary Value Problem ◽  
Positive Solutions ◽  
Fourth Order ◽  
Boundary Value ◽  
Integral Boundary Conditions ◽  
Monotone Iterative Technique ◽  
Iterative Technique ◽  
Integral Boundary ◽  
Monotone Iterative ◽  
Symmetric Positive Solutions

The purpose of this paper is to investigate the existence of symmetric positive solutions for a class of fourth-order boundary value problem:u4(t)+βu′′(t)=f(t,u(t),u′′(t)),0<t<1,u(0)=u(1)=∫01‍p(s)u(s)ds,u′′(0)=u′′(1)=∫01‍qsu′′(s)ds, wherep,q∈L1[0,1],f∈C([0,1]×[0,∞)×(-∞,0],[0,∞)). By using a monotone iterative technique, we prove that the above boundary value problem has symmetric positive solutions under certain conditions. In particular, these solutions are obtained via the iteration procedures.

Multiple symmetric positive solutions to a new kind of four point boundary value problem

2009 ◽  
Vol 71 (1-2) ◽  
pp. 9-18 ◽  
Author(s):  
Junfang Zhao ◽  
Chunmei Miao ◽  
Weigao Ge ◽  
Jiani Zhang
Keyword(s):  
Boundary Value Problem ◽  
Positive Solutions ◽  
Boundary Value ◽  
Point Boundary ◽  
Symmetric Positive Solutions
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