Two Non-negative Solutions Of A Quasilinear Elliptic Equation On R~N

In the paper,we study the existence of solutions of the following quasilinear elliptic equation where N≥ 3, λ€ R. Under suitable assumptions for 7, h(x), V(x),we obtain a Cerami sequence which satisfies the addition condition,by using a new mountain pass theorem,which is used in [14]by C.A.Stuart. Then we used the additional condition to get the boundness and convergence of the sequence, finally we get two non-negative solutions of the quasilinear elliptic equation, one solution is a local minimum and the other is of mountain pass type. In [14],C.A.Stuart studies the following equation: where Ω is a bounded domain in RN, h € L2(f2)and/i> 0 a.e.on Cl. The result we get in this paper is a natural expansion for this result in [14].At the same time,we introduce a weight function which satisfies some conditions.