On the Oscillations of the Solution Curve for A Class of Semilinear Equations
We consider positive solutions of the Dirichlet problem
where B is unit ball in Rn, λ is a positive parameter. Let λ1 denote the principal eigenvalue of the Laplacian on B with zero boundary conditions. We show that for 1⩽n⩽5 the problem has infinitely many positive solutions at λ=λ1, while for n⩾6 the problem has at most finitely many solutions at any λ.
& Li, Y.
(2006). On the Oscillations of the Solution Curve for A Class of Semilinear Equations. Journal of Mathematical Analysis and Applications, 321 (2), 576-588.