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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.
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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