The power potential and nonexistence of positive solutions

Authors

Gisèle Ruiz Goldstein, University of MemphisFollow
Jerome A. Goldstein, University of MemphisFollow
Ismail Kombe, Oklahoma City University

Abstract

We prove the nonexistence of positive solutions of the equation (equation found) for 0 < t < ε and x in a bounded domain in ℝN containing origin. For suitable choices of m < 1 and all γ > −1/2, we show that positive solutions never exist provided c > (N − 2γ − 2)2/4. That is, positive solutions never exist when the c exceeds the best constant for the Hardy inequality corresponding to the linear problem (m = 1).

Publication Title

Differential Equations: Inverse and Direct Problems

Recommended Citation

Goldstein, G., Goldstein, J., & Kombe, I. (2006). The power potential and nonexistence of positive solutions. Differential Equations: Inverse and Direct Problems, 183-195. Retrieved from https://digitalcommons.memphis.edu/facpubs/5938