Supercritical Lane-Emden equation on a cone with an inhomogeneous Dirichlet boundary condition

Autor: Katayama, Sho
Rok vydání: 2024
Předmět:
Druh dokumentu: Working Paper
Popis: We consider the Lane-Emden equation with a supercritical nonlinearity with an inhomogeneous Dirichlet boundary condition on an infinite cone. Under suitable conditions for the boundary data and the exponent of nonlinearity, we give a complete classification of the existence/nonexistence of a solution with respect to the size of boundary data. Moreover, we give a result on the multiple existence of solutions via bifurcation theory. We also state results on Hardy-H\'enon equations on infinite cones as a generalization.
Comment: 29 pages
Databáze: arXiv