Multiplicity of Solutions for Degenerate Nonlocal Problems via Krasnoselskii's Genus
Using the genus theory, introduced by Krasnoselskii, and an application of Palais-Smale
”compactness” criterion , we study the multiplicity of solutions for the degenerate nonlocal problem
Ω |x|−ap|ru|p dx
= |x|−p(a+1)+c f (x,u) in Ω,
u = 0 on ∂Ω,
where Ω RN (N ≥ 3) is a smooth bounded domain, 0 2 Ω, 0 ≤ a < N−p
p , 1 < p < N, c > 0, M : R+ → R+ is a continuous function that may be degenerate at zero.