In this paper we are concerned with the multiplicity of solutions near resonance for the following nonlinear equation:
$ -\Delta u = \lambda u+f(x,u) $
associated with the Dirichlet boundary condition, where $ f $ satisfies some appropriate conditions. We will treat this problem in the framework of dynamical systems. It will be shown that there exist a one-sided neighborhood $ \Lambda_- $ of the eigenvalue $ \mu_k $ of the Laplacian operator and a dense subset $ {\mathcal D} $ of $ \mathbb{R} $ such that the equation has at least four distinct nontrivial solutions generically for $ \lambda\in\Lambda_- \cap {\mathcal D} $.
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