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Volume 9, Number 1, 2019, Pages 12-30                                                                DOI:10.11948/2019.12
Multiple sign-changing solutions for a class of semilinear elliptic equations in $\mathbb{R}^{N}$
Xiumei He,Xian Wu
Keywords:Semilinear elliptic equations, critical point theorem, sign-changing solutions.
Abstract:
      In this paper, we study the following semilinear elliptic equations $$-\triangle u+V(x)u=f(x,u), \ \ x\in \mathbb{R}^{N},$$ where $V\in C(\mathbb{R}^{N}, \mathbb{R})$ and $f\in C(\mathbb{R}^{N}\times\mathbb{R}, \mathbb{R})$. Under some suitable conditions, we prove that the equation has three solutions of mountain pass type: one positive, one negative, and sign-changing. Furthermore, if $f$ is odd with respect to its second variable, this problem has infinitely many sign-changing solutions.
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