Stepanov-like pseudo anti-periodicity and applications to semi-linear
parabolic boundary differential equations
Abstract
This paper is mainly devoted to the existence of pseudo anti-periodic
solutions of parabolic boundary differential equations by the measure
theory. A new class of functions called Stepanov-like (µ0,ν0)-pseudo
anti-periodic functions is proposed, which generalizes the classical
weighted pseudo anti-periodic functions in Stepanov sense. The
completeness of the space composed of these functions is proved.
Translation invariance and two composition theorems are also
established. As an application different from parabolic equations with
linear boundary conditions, one shows that semi-linear parabolic
evolution equations with inhomogeneous boundary conditions admit a
(µ0,ν0)-pseudo anti-periodic solution in interpolation and extrapolation
spaces. An example is presented to verify the existence of pseudo
anti-periodic solution.