Existence and Uniqueness for a Class of SPDEs Driven by L\'{e}vy Noise in Hilbert Spaces

Abstract

The present paper seeks to prove the existence and uniqueness of solutions to stochastic evolution equations in Hilbert spaces driven by both Poisson random measure and Wiener process with non-Lipschitz drift term. The proof is provided by the theory of measure of noncompactness and condensing operators. Moreover, we give some examples to illustrate the application of our main theorem.

Keywords

• poisson random measure
• mild solution
• measure of noncompactness
• condensing operator