Existence of positive solutions for higher order singular sublinear elliptic equations.
Existence of positive solutions for some polyharmonic nonlinear boundary-value problems.
Existence of solutions for a family of polyharmonic and biharmonic equations.
Existence of solutions for an eigenvalue problem with weight.
Existence of the boundary value of a polyharmonic function.
Existence of three solutions for a Navier boundary value problem involving the p(x)-biharmonic operator
The existence of at least three weak solutions is established for a class of quasilinear elliptic equations involving the p(x)-biharmonic operator with Navier boundary value conditions. The proof is mainly based on a three critical points theorem due to B. Ricceri [Nonlinear Anal. 70 (2009), 3084-3089].
Existence of three solutions to a double eigenvalue problem for the p-biharmonic equation
Using a three critical points theorem and variational methods, we study the existence of at least three weak solutions of the Navier problem ⎧ in Ω, ⎨ ⎩u = Δu = 0 on ∂Ω, where (N ≥ 1) is a non-empty bounded open set with a sufficiently smooth boundary ∂Ω, λ > 0, μ > 0 and f,g: Ω × ℝ → ℝ are two L¹-Carathéodory functions.