MULTIPLE SIGN-CHANGING SOLUTIONS FOR A CLASS OF SEMILINEAR ELLIPTIC EQUATIONS IN $\mathbb{R}$<sup><i>N</i></sup>

Xiumei He; Xian Wu

doi:10.11948/2019.12

2019 Volume 9 Issue 1

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Xiumei He, Xian Wu. MULTIPLE SIGN-CHANGING SOLUTIONS FOR A CLASS OF SEMILINEAR ELLIPTIC EQUATIONS IN $\mathbb{R}$N[J]. Journal of Applied Analysis & Computation, 2019, 9(1): 12-30. doi: 10.11948/2019.12

Citation:

Xiumei He, Xian Wu. MULTIPLE SIGN-CHANGING SOLUTIONS FOR A CLASS OF SEMILINEAR ELLIPTIC EQUATIONS IN $\mathbb{R}$^N[J]. Journal of Applied Analysis & Computation, 2019, 9(1): 12-30. doi: 10.11948/2019.12

MULTIPLE SIGN-CHANGING SOLUTIONS FOR A CLASS OF SEMILINEAR ELLIPTIC EQUATIONS IN $\mathbb{R}$^N

Xiumei He^1, ,,
Xian Wu²

1.
Department of Mathematics, Kunming University, Kunming, Yunnan, 650214, China
2.
Department of Mathematics, Yunnan Normal University, Kunming, Yunnan 650092, China

Corresponding author: Email address:hexiumei2004@163.com(X. He)

Abstract

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.
- Semilinear elliptic equations /
- critical point theorem /
- sign-changing solutions
MSC: 35J20, 35J70, 35P05, 35P30, 34B15, 58E05, 47H04

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References

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