Supercritical Lane-Emden equation on a cone with an inhomogeneous Dirichlet boundary condition
Autor: | Katayama, Sho |
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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 |
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