Global solution curves for a class of quasilinear boundary-value problemsProceedings of the Royal Society of Edinburgh Section A: Mathematics (2010)
We use methods of bifurcation theory to study properties of solution curves for a class of quasilinear two-point problems. Unlike semilinear equations, here, solution curves may stop at some point, or solution curves may turn the ‘wrong way’ (compared with semilinear equations) as in a paper by Habets and Omari, where the prescribed mean curvature equation was considered. This class of equations will be our main example. Another difference from semilinear equations is that the bifurcation diagram may depend on the length of the interval, as was discovered recently by Pan, who considered the prescribed mean curvature equation and f(u) = eu. We generalize this result to convex f(u), with f(0) > 0, and to more general quasilinear equations. We also give formulae which allow us to compute all possible turning points and the direction of the turn, generalizing similar formulae in Korman et al. We also present a numerical computation of the bifurcation curves.
Publication DateDecember, 2010
Citation InformationPhilip Korman and Yi Li. "Global solution curves for a class of quasilinear boundary-value problems" Proceedings of the Royal Society of Edinburgh Section A: Mathematics (2010)
Available at: http://works.bepress.com/yi_li/114/