Positive solutions for a nonlocal fourth order equation of Kirchhoff type

To Fu Ma

doi:10.3934/proc.2007.2007.694

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2007, Volume 2007: 694-703. Doi: 10.3934/proc.2007.2007.694 open access

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Positive solutions for a nonlocal fourth order equation of Kirchhoff type

To Fu Ma^1,

1.
Departamento de Matemática, Instituto de Ciências Matemáticas e do Computação, Universidade de São Paulo - Campus de São Carlos, 13560-970 São Carlos, SP

Received: August 31, 2006

Revised: February 28, 2007

Published: August 2007

Abstract Related Papers Cited by

Abstract

Existence and multiplicity of positive solutions for the fourth order equation

$u'''' - M(\eq^1_0 |u'|^2 dx) u'' = q(x)f(x, u, u'),$

which models simply supported extensible beams, are considered using fixed point theorems in cones of ordered Banach spaces.

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Mathematics Subject Classification: Primary: 34B18; Secondary: 34B60.

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