SINGULAR PERTURBATION OF THE FOURTH ORDER ELLIPTIC EQUATION WHEN THE LIMIT EQUATION IS ELLIPTIC-PARABOLIC

3@1In this paper we cosider the singular perturbation of the fourth order elliptic equation-ε~2△~2u+y~m(α~2u)/(αy~2)+(α~2u)/(αx~2)+α(x,y)-(αu)/(αy)+b(x,y)(αu)/(αx)+c(x,y)=0 when the limit equationis elliptic-parabolic,where εis a positive parameter,m is a positive real number,△isLaplacian operator,a.b.c are sufficiently smooth.Under appropriate condition we derivethe sufficient condition of solvability and prove the existence of solution and give auniformly valid asymptotic solution of arbitrary order.