Approximation of the One-Parameter Family of Dirichlet Problems for Higher-Order Elliptic-Type Equations with Discontinuous Nonlinearities in the Resonance Case

摘要

In a number of cases, it is important to analyze the proximity between the solutions of a model with a discontinuous nonlinearity and the solutions of a model with a continuous nonlinearity approximating the initial problem. This problem was posed in [1]; it was studied for coercive elliptic boundary-value problems with discontinuous nonlinearities in [2], [3], and for resonance boundary-value problems, in [4]. Approximations of boundary-value problems for elliptic-type equations with a spectral parameter and a discontinuous nonlinearity were considered in [5]-[7], and a practical example, namely, continuous approximations of the problem of separated flows of incompressible Gol'dshtik fluid, was investigated in [8]. The present paper continues these studies.