Time maps and exact multiplicity results for one-dimensional prescribed mean curvature equations. II

✍ Scribed by Hongjing Pan; Ruixiang Xing

• Publisher: Elsevier Science
• Year: 2011
• Tongue: English
• Weight: 634 KB
• Volume: 74
• Category: Article
• ISSN: 0362-546X
• DOI: 10.1016/j.na.2011.03.020

✦ Synopsis

We consider non-classical solutions of the quasilinear boundary value problem

where λ and L are positive parameters. We give complete descriptions of the structure of bifurcation curves and determine the exact numbers of positive non-classical solutions of the model problems for various nonlinearities

-1, f (u) = u p (p > 0), and f (u) = a u (a > 0). The methods used are elementary and based on a detailed analysis of time maps. Moreover, for the case f (u) = |u| p-1 u(p > 0), we also obtain the exact number of all sign-changing non-classical solutions and show the global structure of bifurcation curves.