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. ) 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.
Variational Inequality Bilinear Form Stochastic Stability Random Vibration Computational Issue
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