Nonlinear evolution equations via resolvent operators on Hadamard manifolds

Abstract

The purpose of this work is to study new systems given by evolution equations via resolvent operators for solving Yosida inclusion problems, equilibrium problems and fixed point problems on Hadamard manifolds. Then we show that the systems have a unique solution under some suitable assumptions. Furthermore, the exponential stability and invariance properties of the systems are also investigated. Our main results in this paper are new and extend the existing ones in the literature.