Linear and nonlinear convolution operator equations on the infinite strip

TL;DR

This paper characterizes the existence, uniqueness, and regularity of solutions for high-order convolution operator equations on an infinite strip, and applies these results to nonlinear integro-differential problems.

Contribution

It provides new conditions for maximal Lp-regular solutions and demonstrates the generation of analytic semigroups for convolution operator equations.

Findings

Established coercive uniform estimates with respect to spectral parameter.

Proved the realization operator is R-positive.

Applied results to nonlinear integro-differential equations.

Abstract

In the present paper we characterize the existence and uniqueness of maximal Lp-regular solutions of high order convolution operator equations. Particularly, we get coercive uniform estimates with respect to spectral parameter and we show that corresponding realization operator is R-positive and generates analytic semigroup in Lp. Then we apply these results to various problems of nonlinear integro-differential equations.