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Monotone Methods Applied to Some Higher Order Boundary Value Problems  
 
  Authors: John M. Davis, Johnny Henderson,  
  Keywords: Differential Inequality, Monotone Methods, Upper and Lower Solutions, Maximum Principle  
  Date Received: 26/06/00  
  Date Accepted: 06/07/00  
  Subject Codes:

34B15,34A40,34C11,34C12

  
  Editors: Ravi P. Agarwal,  
 
  Abstract:

We prove the existence of a solution for the nonlinear boundary value problem

  $displaystyle u^{(2m+4)}=fleft(x,u,u'',dots,u^{(2m+2)}ight), qquad x in [0,1],$  
  $displaystyle u^{(2i)}(0)=0=u^{(2i)}(1), qquad 0le ile m+1,$  

where $ f:[0,1]times{mathbb{R}}^{m+2}o{mathbb{R}}$ is continuous. The technique used here is a monotone method in the presence of upper and lower solutions. We introduce a new maximum principle which generalizes one due to Bai which in turn was an improvement of a maximum principle by Ma.;


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