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Existence of solutions and bifurcation points to Hammerstein equations with essentially bounded kernel. (English) Zbl 1067.45001
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 Carathéodory function. The proofs rely on the Tychonoff fixed point theorem.

MSC:
45G10 Other nonlinear integral equations
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