Multiplicity results for solutions of p-biharmonic problems. (January 2020) - Lu, Yao; Fu, Yongqiang
Abstract: In this paper, we deal with the multiplicity existence of solutions for the following p -biharmonic equation: Δ p 2 u = λ | u | p − 2 u + | u | q − 2 u, in Ω, u = Δ u = 0, on ∂ Ω, where Ω is a bounded domain in R N, Δ p 2 u = Δ ( | Δ u | p − 2 Δ u ), p < q ≤ p ∗ = N p N − 2 p, λ ∈ R is a parameter. When p < q < p ∗, we prove that the above problem possesses infinitely many solutions. While when q = p ∗, a multiplicity existence result is obtained.