id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejde-1570	Wei, Qifan; Zhang, Xuemei	Existence and multiplicity of solutions to triharmonic problems	2025	21	.pdf	application/pdf	9361	555	81	In particular, by using a variant version of the mountain pass lemma, Hu-Wang [29] obtained the existence of nontrivial solutions for the following fourth-order problem ∆2u+ α∆u = f(x, u) in Ω, u = ∆u = 0 on ∂Ω, (1.3) where ∆2(u) = ∆(∆u) stands for the biharmonic operator, Ω ⊂ RN (N > 4) is a smooth bounded domain, and α < µ1 is a parameter, where µ1 is the first eigenvalue of (−∆) in H1 0 (Ω). [37] studied the fourth-order problem ∆2u+ β∆u = a(x)|u|s−2u+ f(x, u) in Ω, u = ∆u = 0 on ∂Ω, (1.4) where Ω ⊂ RN (N > 4) is a smooth bounded domain, β < µ1, a(x) ∈ L∞(Ω), s ∈ (1, 2) and f ∈ C(Ω̄ × R,R).	cache/ejde-1570.pdf	txt/ejde-1570.txt