Nonlinear Leray-Schauder alternatives and application to nonlinear problem arising in the theory of growing cell population (Q657378)

The author uses the Leray-Schauder theory in order to study existence and locality for the following biological model arising in the theory of growing cell populations: \[ \lambda\phi(a,l)+\frac{\partial\phi}{\partial a}+\sigma(a,l)\phi(a,l)=\int_{l_1}^{l_2}r(a,l,l',\phi(a,l'))dl' \] in the open rectangle \(D=(0,l)\times(l_1,l_2)\) where \(\sigma\in L^\infty(D)\) and \(\lambda\in\mathbb{C}\).