an:07184992
Zbl 1436.35195
Chen, Yutong; Su, Jiabao; Sun, Mingzheng; Tian, Rushun
Multiple solutions for the coercive semilinear elliptic equations
EN
J. Math. Anal. Appl. 487, No. 2, Article ID 124031, 12 p. (2020).
00448228
2020
j
35J91 35A01
semilinear elliptic equation with Laplacian; Dirichlet problem; existence of solutions
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.