In this paper we study the existence of mild and classical solutions for a second-order abstract Cauchy problem with nonlocal conditions.

We show that weak (Eulerian) solutions for the Semi-Geostrophic system in physical space exhibiting some mild regularity in time cannot yield point masses in dual space. However, such solutions are physically relevant to the model. Thus, we discuss a natural generalization of weak Lagrangian solutions in the physical space to include the possibility of singular measures in dual space. We prove ...

We discuss the existence of solutions for second-order impulsive differential equation with nonlocal conditions in Banach spaces. Our approach is based on generalization Schauder fixed pointprinciple that Darbo point theorem. An example also presented to illustration.

In this paper we study the existence of mild solutions for a class of abstract partial neutral integro-differential equations with state-dependent delay.