Jean Mawhin, Institut de Recherche en Mathématique et Physique, Université Catholique de Louvain, chemin du Cyclotron, 2, B-1348 Louvain-la-Neuve, Belgium, e-mail: jean.mawhin@uclouvain.be
Abstract: The paper surveys recent results obtained for the existence and multiplicity of radial solutions of Dirichlet problems of the type
\nabla\cdot\bigg(\frac{\nabla v}{\sqrt{1 - |\nabla v|^2}}\bigg) = f(|x|,v) \quad\text{in} B_R,\quad u = 0 \quad\text{on} \partial B_R ,
where $B_R$ is the open ball of center $0$ and radius $R$ in $\mathbb R^n$, and $f$ is continuous. Comparison is made with similar results for the Laplacian. Topological and variational methods are used and the case of positive solutions is emphasized. The paper ends with the case of a general domain.
Keywords: extrinsic mean curvature operator; Dirichlet problem; radial solution; positive solution; Leray-Schauder degree; critical point theory
Classification (MSC 2010): 35J20, 35J60, 35J93, 35J87
Full text available as PDF.
Access to the full text of journal articles on this site is restricted to the subscribers of Myris Trade. To activate your access, please contact Myris Trade at myris@myris.cz.
