This article studies the qualitative and quantitative properties of radial solutions to an elliptic equation related to the Euler–Lagrange equations for certain sharp Caffarelli–Kohn–Nirenberg inequalities. Namely, we examine the equation
−div(|x|aDu)=|x|bup, u>0, in RN, where p>1, N≥2, N−2+a≥0 and b>−N. The main results establish the properties of radially symmetric solutions including existence, uniqueness, and classification results as well as results on the asymptotic and intersecting behaviour of such solutions.
Villavert, John, "Classification of radial solutions to equations related to Caffarelli–Kohn–Nirenberg inequalities" (2020). Mathematical and Statistical Sciences Faculty Publications and Presentations. 21.
Annali di Matematica