In this paper, we establish two results assuring that $\lambda=0$ is a bifurcation point in $L^\infty(\Omega)$ for the Hammerstein integral equation \begin{center} $u(x)=\lambda\int_\Omega k(x,y)f(y,u(y))dy.$ \end{center} We also present an application to the two-point boundary value problem $\left\{ \begin{array}{ll} -u''=\lambda f(x,u) & \mbox{a.e. in [0,1] } \\ u(0)=u(1)=0 \end{array} \right.$

### Bifurcation theorems for Hammerstein nonlinear integral equations

#### Abstract

In this paper, we establish two results assuring that $\lambda=0$ is a bifurcation point in $L^\infty(\Omega)$ for the Hammerstein integral equation \begin{center} $u(x)=\lambda\int_\Omega k(x,y)f(y,u(y))dy.$ \end{center} We also present an application to the two-point boundary value problem $\left\{ \begin{array}{ll} -u''=\lambda f(x,u) & \mbox{a.e. in [0,1] } \\ u(0)=u(1)=0 \end{array} \right.$
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/20.500.11769/4780
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