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Positive solutions for a nonlocal fourth order equation of Kirchhoff type

Pages: 694 - 703, Issue Special, September 2007

 Abstract        Full Text (208.0K)              

To Fu Ma - Departamento de Matemática, Instituto de Ciências Matemáticas e do Computação, Universidade de São Paulo - Campus de São Carlos, 13560-970 São Carlos, SP, Brazil (email)

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.

Keywords:  Beam equation, fixed point theorem, multiple solutions.
Mathematics Subject Classification:  Primary: 34B18; Secondary: 34B60.

Received: September 2006;      Revised: March 2007;      Published: September 2007.