Electron. J. Differential Equations, Vol. 2017 (2017), No. 275, pp. 1-11.

Multiple positive solutions for a nonlocal problem involving critical exponent

Yue Wang, Hong-Min Suo, Chun-Yu Lei

Abstract:
This article concerns the nonlocal problem
$$\displaylines{ -\Big(a-b\int_{\mathbb{R}^4}|\nabla u|^2\,dx\Big)\Delta u=|u|^2u+\mu f(x), \quad\text{in }\mathbb{R}^4,\cr u\in \mathcal{D}^{1,2}(\mathbb{R}^4), }$$
where a, b are positive constants, $\mu$ is a non-negative parameter, $f(x)\in L^{4/3}(\mathbb{R}^4)$ is a non-negative function. By using the variational method, the existence of multiple positive solutions are obtained.

Submitted August 15, 2017. Published November 5, 2017.
Math Subject Classifications: 35A15, 35B09, 35B33.
Key Words: Multiple positive solutions; nonlocal problem; critical exponent.

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Yue Wang
School of Data Science and Information Engineering
Guizhou Minzu University
Guiyang 550025, China
email: wyeztf@gmail.com
Hong-Min Suo
School of Data Science and Information Engineering
Guizhou Minzu University
Guiyang 550025, China
email: 11394861@qq.com
Chun-Yu Lei
School of Data Science and Information Engineering
Guizhou Minzu University
Guiyang 550025, China
email: leichygzu@sina.cn

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