This paper is concerned with the existence of global mild solutions and positive mild solutions to initial value problem for a class of mixed type semilinear evolution equations with noncompact semigroup in Banach spaces. The main method is based on a new fixed point theorem with respect to convex-power condensing operator.
SHI, HONG-BO; LI, WAN-TONG; and SUN, HONG-RUI
"Existence of mild solutions for abstract mixed type semilinear evolution equations,"
Turkish Journal of Mathematics: Vol. 35:
3, Article 9.
Available at: https://journals.tubitak.gov.tr/math/vol35/iss3/9