Abstract
In this paper, we study the nonhomogeneous elliptic equations $-\Delta u(x)+u(x)=\lambda (f(x,u)+h(x))$ in ${\mathbb R}^{N}$, where $f(x,u)$ and $h(x)$ satisfy some assumptions. We use variational methods to obtain the existence results and give a clever argument to establish the exact number of solutions. In addition to a lack of compactness the main difficulty to overcome is the degenerated structure of the set of possible critical points.
Citation
Kuan-Ju Chen. "Exactly two entire positive solutions for a class of nonhomogeneous elliptic equations." Differential Integral Equations 17 (1-2) 1 - 16, 2004. https://doi.org/10.57262/die/1356060469
Information