Singular solutions for Lane–Emden equations with CKN operator

Abstract

In this paper, we concern the isolated singular solutions for Lane–Emden equations involving the CKN operator We classify the isolated singularities by building the connection with the equations involving the Dirac mass in a weighted distributional sense. Then, we obtain the minimal singular solution with given singularities at the origin, analyze the stability of the minimal singular solutions. Finally, we can derive a second solution by the variational method with the given singularities.