Approximation to the Dirichlet Problem for a Higher-Order Elliptic Equation with a Spectral Parameter and a Discontinuous Nonlinearity

摘要

Models with discontinuous nonlinearities arise as idealization of continuous processes whose nonlinear parameters rapidly vary on small intervals in the range of the phase variable. As a rule, it is impossible to trace changes of parameters on such intervals; therefore, the process parameters are replaced by a discontinuous nonlinearity on each of these intervals. It is natural to ask whether the solutions of the equation with idealized characteristics and those of the equation with the original parameters are close. For the importance of this problem, see [1].