Nonlocal evolution inclusions under weak conditions

Abstract

Abstract We study evolution inclusions given by multivalued perturbations of m-dissipative operators with nonlocal initial conditions. We prove the existence of solutions. The commonly used Lipschitz hypothesis for the perturbations is weakened to one-sided Lipschitz ones. We prove an existence result for the multipoint problems that cover periodic and antiperiodic cases. We give examples to illustrate the applicability of our results.

Keywords

• m-dissipative evolution inclusions
• Nonlocal initial conditions
• One-sided Lipschitz condition