SEMILINEAR EVOLUTION EQUATIONS WITH NONLOCAL INITIAL CONDITIONS

We are concerned with the study of semilinear evolution equations with nonlocal initial conditions. We provide sufficient conditions on the nonlinearity which allow the use of variants of the nonlinear alternative to prove the existence of at least one solution. Our second result presents a novel growth condition splitted into two parts, one for the subinterval containing the points involved by the initial conditions, and another for the rest of the interval.