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Bifurcation theorems for Hammerstein nonlinear integral equations

Published online by Cambridge University Press:  26 February 2003

Francesca Faraci
Francesca Faraci
Affiliation:
Department of Mathematics & Computer Science, University of Catania, Viale A.Doria, 6, 95125 Catania, Italy e-mail: ffaraci@dmi.unict.it
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In this paper, we establish two results assuring that \lambda =0 is a bifurcation point in L^ \rm{inf} ty (\Omega ) for the Hammerstein integral equation

u(x)=\lambda \int _\Omega k(x,y)f({}y,u({}y))dy.

We also present an application to the two-point boundary value problem

\cases{ -u''=\lambda f(x,u)\hfill \hbox {a.e. in [0,1] } \cr u(0)=u(1)=0 } \right.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 44 , Issue 3 , September 2002 , pp. 471 - 481
Copyright
2002 Glasgow Mathematical Journal Trust