id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejde-974	Xie, Junhui; Li, Pengfei	Existence of solutions to fractional p-Laplacian problems with Robin boundary conditions	2025	17	.pdf	application/pdf	7060	350	86	Hence g′(t) = −tr−p−1(r − q)(r − p) ∫ Ω |u|r |x|α dx < 0. On the contrary, ifN0 λ ̸= ∅, then there exists u ∈ N0 λ, this implies ⟨Ψ′(u), u⟩ = 0, we can deduce that (p− q)∥u∥p Xs,p β ≤ (p− q)∥u∥p Xs,p β + (p− q) ∫ Rn\Ω β(x)|u|pdx = (r − q) ∫ Ω |u|r |x|α dx, (3.3) EJDE-2025/13 SOLUTIONS TO FRACTIONAL P-LAPLACIAN PROBLEMS 7 and (r − p)∥u∥p Xs,p β ≤ (r − p)∥u∥p Xs,p β + (r − p) ∫ Rn\Ω β(x)|u|pdx = (r − q)λ ∫ Ω |u|qdx. (3.4) By (2.2), we obtain (r − q) ∫ Ω |u|r |x|α dx ≤ (r − q)S−r/p α Ĉ−1∥u∥rXs,p β .	cache/ejde-974.pdf	txt/ejde-974.txt