On a Class of Partial Differential Equations with Nonlocal Dirichlet Boundary Conditions

We establish existence and uniqueness of solutions of a class of partial differential equations with nonlocal Dirchlet conditions in weighted function spaces. The problem is motivated by the study of the probability distribution of the response of an elasto-plastic oscillator when subjected to white noise excitation (see [1,2] on the derivation of the boundary value problem). Note that the developments in [1,2] are based on an extension of Khasminskii's method (see, e.g. [5]) and in this paper we use a direct approach to achieve our objectives. We refer the reader to [3, 4, 6, 7] for general background on modeling, theoretical, and computational issues related to elasto-plastic oscillators.