an:02117742
Zbl 1067.45001
Anello, Giovanni; Cordaro, Giuseppe
Existence of solutions and bifurcation points to Hammerstein equations with essentially bounded kernel
EN
J. Math. Anal. Appl. 298, No. 1, 292-297 (2004).
00110146
2004
j
45G10
Hammerstein equations; bifurcation point; fixed point; essentially bounded kernel
This paper deals with an existence theorem of solutions and of bifurcation points for the Hammerstein integral equation
\[
u(x)=\lambda\int_{\Omega}k(x,y)f(y,u(y))dy,
\]
where \(\lambda\in \mathbb R\), \(\Omega\) is a Lebesgue measurable subset of \(\mathbb R^{n}, \;k\in L^{\infty}(\Omega\times\Omega)\) and \(f:\Omega\times \mathbb R\to \mathbb R\) is a Carath??odory function. The proofs rely on the Tychonoff fixed point theorem.
Mouffak Benchohra (Sidi Bel Abbes)