Electron. J. Differential Equations, Vol. 2022 (2022), No. 75, pp. 1-13.

Positive solutions for Kirchhoff-Schrodinger equations via Pohozaev manifold

Xian Hu, Yong-Yi Lan

Abstract:
In this article we consider the Kirchhoff-Schrodinger equation

where $u\in H^{1}(\mathbb{R}^3)$, $\lambda >0$, $a>0$, $b\geq 0$ are real constants, $k:\mathbb{R}^3\to \mathbb{R}$ and $f \in \mathcal{C}(\mathbb{R},\mathbb{R})$. To overcome the difficulties that k is non-symmetric and the non-linear, and that f is non-homogeneous, we prove the existence a positive solution using projections on a general Pohozaev type manifold, and the linking theorem.

Submitted March 21, 2022. Published November 17, 2022.
Math Subject Classifications: 35J35, 35B38, 35J92.
Key Words: Kirchhoff-Schrodinger equation; Pohozaev manifold; Cerami sequence; linking theorem.
DOI: https://doi.org/10.58997/ejde.2022.75

Show me the PDF file (345 KB), TEX file for this article.

Xian Hu
School of Sciences
Jimei University
Xiamen 361021, China
email: huxian19972021@163.com
Yong-Yi Lan
School of Sciences
Jimei University
Xiamen 361021, China
email: lanyongyi@jmu.edu.cn

Return to the EJDE web page