Existence of positive periodic solutions for abstract evolution equations

Qiang Li, Yongxiang Li
2015 Advances in Difference Equations  
In this paper, we discuss the existence of the positive time periodic mild solutions for the evolution equation in an ordered Banach space E, We apply the operator semigroup theory and the Leray-Schauder fixed point theorem to obtain the existence of a positive ω-periodic mild solution under the condition that the nonlinear function satisfies a linear growth condition concerning the growth exponent of the semigroup T(t) (t ≥ 0). In the end, an example is given to illustrate the applicability of
more » ... our abstract results. MSC: 34K30; 47H07; 47H08 Keywords: abstract evolution equation; positive periodic mild solutions; positive compact semigroup; the growth exponent of the semigroup; fixed point theorem
doi:10.1186/s13662-015-0435-5 fatcat:kpnqzf52ivhx7al6dlydqudume