Abstract: In this paper,starting from some fundamental properties of Heaviside function and δ -function,making use of singular perturbation methods we provide a method of finding the asymptotic analytic solution of equationwhere M(u)=eƒ+λ#948;(t-a) is an n -order linear differential operator,ƒ(u) is a polynomial. By means of this method,we discuss some examples concretely. The results can be explained satisfactorily in physics. If we deal with linear problem by this method,the result will agree with that drawn from theorem of impulse.

Key words: bilevel generalized mixed equilibrium problem (BGMEP), generalized mixed variational-like inequality problem (GMVLIP), auxiliary principle, iterative algorithm, reflexive Banach space