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Multiplicity of Solutions for Degenerate Nonlocal Problems via Krasnoselskii's Genus

Volume 4, Number 1 (2013), 58 - 66

Multiplicity of Solutions for Degenerate Nonlocal Problems via Krasnoselskii's Genus

Communicated By: 
Irena Lasiecka
Price: $20.00

Abstract

Using the genus theory, introduced by Krasnoselskii, and an application of Palais-Smale
”compactness” criterion [7], we study the multiplicity of solutions for the degenerate nonlocal problem
8>>>><>>>>:
−M
Z
Ω |x|−ap|ru|p dx
!
|x|−ap|ru|p−2ru

= |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.