Monotone iterative techniques for parameterized BVPs of abstract semilinear evolution equations

This paper is concerned with parameterized boundary value problems (BVPs) for semilinear evolution equations in a general Banach space. The abstract monotone iterative schemes are constructed by combining the theory of semigroups of operators and the method of upper and lower solutions. Some existence results are established under the suitable conditions. Applications to periodic BVPs with a parameter and parabolic partial differential equations are also given to illustrate the main results.