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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.;


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