Symmetric mountain pass lemma and sublinear elliptic equations

In this paper, we study the p-Laplace elliptic equations under the Dirichlet boundary condition. We give a general and weak sufficient condition for the existence of a sequence of solutions converging to zero. This result is proved by applying the symmetric mountain pass lemma obtained in our earlier paper. For some elliptic equations with parameters, we decide whether the zero solution is an accumulation point or an isolated point in the set of all solutions.