In this paper, we present some results regarding existence and uniqueness of solution on L p -spaces, 1 < p < +∞, to a nonlinear initial boundary value problem originally proposed by Lebowitz and Rubinow (J Math Biol 1:17-36, 1974) to model an age-structured cell population with inherited properties. Our results complete those obtained by Garcia
In this paper, we establish two fixed point theorems of Himmelberg's type for multivalued maps. Using abstract measures of weak noncompactness, these results are applied to derive some fixed point theorems of Sadovskii's type.
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