Work

Entire solutions and global bifurcations for a biharmonic equation with singular non-linearity in $\Bbb R^3$

Year: 2008

Type: article

Abstract: We study the structure of solutions of the boundary-value problem \begin{equation} \tag*{(0.1)} \Delta^2 u=\frac{\lambda}{(1-u)^2} \;\; \mbox{in $B$}, \;\;\; u=\Delta u=0 \;\; \mbox{on $\partial B$} , \end{equation} where $\Delta^2$ is the biharmonic operator and $B \subset \mathbb R^3$ is the unit ball. We show that there are infinitely many turning points of the branch of the radial solutions of (0.1). The structure of solutions depends on the classification of the radial solutions of the equation \begin{equation} \tag*{(0.2)} -\Delta^2 u=u^{-2} \;\;\; \mbox{in $\mathbb R^3$}. \;\; \end{equation} This is in sharp contrast with the corresponding result in $\mathbb R^2$.

Source: Advances in Differential Equations

DOI: 10.57262/ade/1355867335

Authors: Zongming Guo, Juncheng Wei

Institutions: Chinese University of Hong Kong, Henan Normal University

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: bronze

Funder: National Natural Science Foundation of China

Award: 一类非线性偏微分方程(组)的解的结构及性质的研究