The power potential and nonexistence of positive solutions
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).
Differential Equations: Inverse and Direct Problems
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