Measure (ω, c)‐Pseudo‐Almost Periodic Functions and Lasota‐Wazewska Model with Ergodic and Unbounded Oscillating Oxygen Demand

The primary aim of this work is to introduce a new class of functions called μ‐(ω, c)‐pseudo‐almost periodic functions. Using the measure theory, we generalize in a natural way some recent works and study some properties of those μ‐(ω, c)‐pseudo‐almost periodic functions including two new composition results which play a crucial role for the existence of some μ‐(ω, c)‐pseudo‐almost periodic solutions of certain semilinear differential equations and partial differential equations. We also investigate the existence and uniqueness of the μ‐(ω, c)‐pseudo‐almost periodic solutions for some models of Lasota‐Wazewska equation with measure (ω, c)‐pseudo‐almost periodic coefficient and mixed delays.