Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4623247 | Journal of Mathematical Analysis and Applications | 2006 | 13 Pages |
Abstract
We consider positive solutions of the Dirichlet problemΔu+λ(u+sinu)=0,x∈B,u=0forx∈∂B, where B is unit ball in RnRn, λ is a positive parameter. Let λ1λ1 denote the principal eigenvalue of the Laplacian on B with zero boundary conditions. We show that for 1⩽n⩽51⩽n⩽5 the problem has infinitely many positive solutions at λ=λ1λ=λ1, while for n⩾6n⩾6 the problem has at most finitely many solutions at any λ.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Anahit Galstian, Philip Korman, Yi Li,