＜正＞ The purpose of this paper is to study the existence of the classical solutions of someDirichlet problems for quasilinear elliptic equationsa11（x,y,u）（ ~2u）/（ x~2）+2a12（x,y,u）)（ ~2u）/（ x y）+a22（x,y,u）（ ~2u）/（ y~2）+f（x,y,u,（ u）/（ x）,（ u）/（ y））=0where aij（x,y,u）（i,j=1,2）satisfyλx,y,u丨ξ丨~2≤ aij（x,y,u）ξiξj≤Λ（x,y,u）丨ξ丨~2for all ξ∈R~2 and （x,y,u）∈×[0,+∞),i.e.,λ.（x,y,u）、A（x,y,u）denote the minimumand maximum eigenvalues of the matrix[aij（x,y,u）]respectively,moreoverλ（x,y,0）=0;Λ（x,u,0）=0;Λ（x,y,u）≥λ（x,y,u）＞0,（u＞0）.Some existence theorems under the “natural conditions” imposed on f（x,y,u,p,q）are obtained.
展开▼
