Volume 2,  Issue 1, 2001

Article 2

MONOTONE METHODS APPLIED TO SOME HIGHER ORDER BOUNDARY VALUE PROBLEMS

JOHN M. DAVIS AND JOHNNY HENDERSON

DEPARTMENT OF MATHEMATICS
BAYLOR UNIVERSITY
WACO, TX  76798
E-Mail: John_M_Davis@baylor.edu

DEPARTMENT OF MATHEMATICS
AUBURN UNIVERSITY
AUBURN, AL 36849
E-Mail: hendej2@mail.auburn.edu

Received 26 June, 2000; accepted 6 July, 2000.
Communicated by: R.P. Agarwal


ABSTRACT We prove the existence of a solution for the nonlinear boundary value problem
  $\displaystyle u^{(2m+4)}=f\left(x,u,u'',\dots,u^{(2m+2)}\right), \qquad x\in[0,1],$    
  $\displaystyle u^{(2i)}(0)=0=u^{(2i)}(1), \qquad 0\le i\le m+1,$    

where $ f:[0,1]\times{\mathbb{R}}^{m+2}\to{\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.
Key words:
Differential Inequality, Monotone Methods, Upper and Lower Solutions, Maximum Principle

2000 Mathematics Subject Classification: 34B15, 34A40, 34C11, 34C12


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Some inequalities for the dispersion of a random variable whose PDF is defined on a finite interval
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Monotone Methods Applied to Some Higher Order Boundary Value Problems
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On Multiplicatively Perfect Numbers
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Some Aspects of Convex Functions and Their Applications
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Further Reverse Results for Jensen's Discrete Inequality and Applications in Information Theory
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Sharp Bounds on Quasiconvex Moments of Generalized Order Statistics 
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Inequalities on Polynomial Heights
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An Application of Van der Corput's Inequality
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On a Inequality of Gronwall
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Complete Systems of Inequalities
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On Some Applications of the AG Inequality in Information Theory
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On Ky Fan's Minimax Inequalities, Mixed Equilibrium Problems and Hemivariational Inequalities
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