Abstract: We establish the existence and multiplicity of weak solutions for equations which involve a uniformly convex elliptic operator in divergence form（in particular, a p-Laplacian operator）, while the nonlinearity has a（p- 1）-superlinear growth at infinity. Our result completes and extends the relevant results of recent papers. The argument in the proof of our main result relies on the Z2-symmetric version of mountain pass lemma. 

Key words: variational method, uniformly convex, divergence type operator, symmetric mountain pass lemma