JIPAM logo: Home Link
 
Home Editors Submissions Reviews Volumes RGMIA About Us
 

   
  Volume 10, Issue 1, Article 9
 
Positive solutions for Second-Order Boundary Value Problem with Integral Boundary Conditions at Resonance on a Half-Line
    Authors: Aijun Yang, Weigao Ge,  
    Keywords: Boundary value problem; Resonance; Cone; Positive solution; Coincidence.  
    Date Received: 03/02/09  
    Date Accepted: 25/02/09  
    Subject Codes:

34B10; 34B15; 34B45

  
    Editors: Ravi P. Agarwal,  
 
    Abstract:

This paper deals with the second order boundary value problem with integral boundary conditions on a half-line:

$displaystyle (p(t)x^{prime}(t))^{prime}+ g(t)f(t,x(t))=0, $a.e. in $displaystyle (0,infty),$
$displaystyle x(0)=int_{0}^{infty}x(s)g(s)ds,qquad lim limits_{tightarrowinfty}p(t)x^{prime}(t)=p(0)x^{prime}(0).$
A new result on the existence of positive solutions is obtained. The interesting points are: firstly, the boundary value problem involved in the integral boundary condition on unbounded domains; secondly, we employ a new tool - the recent Leggett-Williams norm-type theorem for coincidences and obtain positive solutions. Also, an example is constructed to illustrate that our result here is valid.

         
       
  Download Screen PDF
  Download Print PDF
  Send this article to a friend
  Print this page
  

      search [advanced search] copyright 2003 terms and conditions login