The Nehari manifold for a quasilinear polyharmonic equation with exponential nonlinearities and a sign-changing weight function

Abstract

AbstractIn this article, we consider the following quasilinear polyharmonic equation: Δn/mmu = λh(x)|u|q-1u + u|u|pe|u|β in Ω, u = ∇u = ⋯ = ∇m-1u = 0 on ∂Ω, where Ω ⊂ ℝn, n ≥ 2m ≥ 2, is a bounded domain with smooth boundary. The real-valued function h is a sign-changing and unbounded function. The exponents p, q and β satisfy 0 < q < n/(m-1) < p+1, β ∈ (1,n/(n-m)] and λ > 0. Using the Nehari manifold and fibering maps, we show the existence and multiplicity of solutions.