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Multiple solutions for the coercive semilinear elliptic equations. (English) Zbl 1436.35195
Summary: In this paper we study the semilinear elliptic equations $\begin{cases} - \Delta u = f(x,u), & \quad x \in \Omega, \\ u = 0, & \quad x \in \partial \Omega, \end{cases}$ where $$\Omega \subset \mathbb{R}^N$$ is a smooth bounded domain. By using the minimax methods, bifurcation methods, Conley index theory and Morse theory, we obtain six nontrivial solutions for the equations with coercive nonlinearities.
##### MSC:
 35J91 Semilinear elliptic equations with Laplacian, bi-Laplacian or poly-Laplacian 35A01 Existence problems for PDEs: global existence, local existence, non-existence
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