Analysis of an Emden-Fowler-Hénon type equation
Abstract
This work investigates a Hénon-type equation with the cap-shaped weight Vα(|x|)=(4|x|(1-|x|))α, which concentrates on the sphere of radius 1/2 as α∞. Particular attention is devoted to ground state solutions and the phenomenon of symmetry breaking in the large-α regime. A complete description of the asymptotic behavior of ground state radial solutions is obtained as α∞. The analytical results are further supported by numerical simulations of the radial ground states.
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