On some fourth-order semilinear elliptic problems in

EXISTENCE OF THREE SOLUTIONS FOR A CLASS OF NAVIER QUASILINEAR ELLIPTIC SYSTEMS INVOLVING THE (p1, …, pn)-BIHARMONIC

“…More general nonlinear fourth-order elliptic boundary value problems have been studied [5,7,16,17]. Particularity, Li and Tang [13] consider the p-harmonic equation with Navier boundary condition.…”

Multiplicity of Solutions for Biharmonic Elliptic Systems Involving Critical Nonlinearity

“…Many important results were obtained in these publications (see [3,5,7,9,10,11,18,21,23] and the references therein). For example, Edmunds, et al [7] showed that, if q = 2, the equation (1.2) has a nontrivial solution provided N ≥ 8 and 0 < λ < λ 1 , where λ 1 is the first eigenvalue of the operator (∆ 2 , H 2 0 (Ω)).…”

Existence of three solutions for p-biharmonic equation

“…Due to (j 3 ), for each λ > 0, it appears that 8) and therefore the first assumption of Theorem 2.1 holds true. Due to Lemma 2.1, there exists u * ∈ X such that …”