Continuous Dependence on Data for a Second-Order Nonhomogeneous Difference Inclusion

We wish to investigate the continuous dependence on data for a nonhomogeneous second-order difference inclusion corresponding to a general second-order evolution equation of accretive type in a Banach space. Our conclusions are new even for Hilbert spaces and significantly extend some previously known results to the nonhomogeneous case by assuming much weaker conditions on the zeroes of operators. Applicability of our results is demonstrated through a partial-difference equation example.

Automated summary

This paper investigates the continuous dependence on data for a nonhomogeneous second-order difference inclusion corresponding to a general second-order evolution equation of accretive type in a Banach space. The conclusions obtained in this study are new and significantly extend some previously known results to the nonhomogeneous case by assuming weaker conditions on the zeroes of operators. The applicability of the results is demonstrated through an example of a partial-difference equation.