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In this article, we apply the perturbation technique and monotone iterative method in the presence of the lower and the upper solutions to discuss the existence of the minimal and maximal mild solutions to the retarded evolution equations involving nonlocal and impulsive conditions in an ordered Banach space X $$\displaylines{ u'(t)+Au(t)= f(t,u(t),u_t),\quad t\in [0,a],\; t\neq t_k,\cr u(t_k^+)=u(t_k^-)+I_k(u(t_k)),\quad k=1,2,\dots ,m,\cr u(s)=g(u)(s)+\varphi(s),\quad s\in [-r,0], }$$ where $A:D(A)\subset X\to X$ is a closed linear operator and -A generates a strongly continuous semigroup T(t) $(t\geq 0)$ on X, a, r>0 are two constants, $f:[0,a]\times X\times C_0\to X$ is Caratheodory continuous, $0

In this article, we study the existence of piecewise-continuous mild solutions for the initial value problems for a class of semilinear evolution equations. These equations have non-instantaneous impulses in Banach spaces and the corresponding solution semigroup is noncompact. We assume that the nonlinear term satisfies certain local growth condition and a noncompactness measure condition. Also we assume the non-instantaneous impulsive functions satisfy some Lipschitz conditions. An example is given to illustrate our results.

The aim of this article is to study the existence and uniqueness of strong solutions for a class of semilinear evolution equations with nonlocal initial conditions. The discussions are based on analytic semigroup theory and fixed point theorems. An example illustrates the main results.

By using monotone iterative technique and operator semigroup theorem, we consider the existence of mild solutions for a class of nonlocal semi-linear evolution equation with not instantaneous impulses in ordered Banach spaces. Finally, an example is given to show the existence results. [ABSTRACT FROM AUTHOR]