Locating the Peaks of Least-Energy Solutions to a Quasi-Linear Elliptic Neumann ProblemJournal of Mathematical Analysis and Applications
AbstractIn this paper we study the shape of least-energy solutions to the quasilinear problem εmΔmu−um−1+f(u)=0 with homogeneous Neumann boundary condition. We use an intrinsic variation method to show that as ε→0+, the global maximum point Pε of least-energy solutions goes to a point on the boundary ∂Ω at the rate of o(ε) and this point on the boundary approaches to a point where the mean curvature of ∂Ωachieves its maximum. We also give a complete proof of exponential decay of least-energy solutions.
Citation InformationChunshan Zhao and Yi Li. "Locating the Peaks of Least-Energy Solutions to a Quasi-Linear Elliptic Neumann Problem" Journal of Mathematical Analysis and Applications Vol. 72 Iss. 11 (2010) p. 4188 - 4199
Available at: http://works.bepress.com/chunshan_zhao/16/