Electronic Journal of Differential Equations, Vol. 2022 (2022), No. 75, pp. 1-13.

Title: Positive solutions for Kirchhoff-Schrodinger equations via Pohozaev manifold
       
Authors: Xian Hu     (Jimei Univ., Xiamen, China)
         Yong-Yi Lan (Jimei Univ., Xiamen, China)
         
Abstract:  
 In this article we consider the Kirchhoff-Schrodinger equation
 $$
 -\Big((a+b\int_{\mathbb{R}^3}|\nabla u|^2\,dx\Big)\Delta u
 +\lambda u=k(x)f(u),\quad x\in \mathbb{R}^3,
 $$
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.