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Motivated by a mathematical model of an age structured proliferating cell population, we state some new variants of Leray-Schauder type fixed point theorems for (ws)-compact operators. Further, we apply our results to establish some new existence and locality principles for nonlinear boundary value problem arising in the theory of growing cell population in L1-setting. Besides, a topological structure of the set of solutions is provided.

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