On the Oscillations of the Solution Curve for A Class of Semilinear Equations

Authors

Anahit Galstian
Philip Korman
Yi Li, Wright State University - Main CampusFollow

Document Type

Article

Publication Date

9-2006

Abstract

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.

Repository Citation

Galstian, A., Korman, P., & 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.
https://corescholar.libraries.wright.edu/math/96

DOI

dx.doi.org/10.1016/j.jmaa.2005.08.074