On Fourth-Order Elliptic Equations of Kirchhoff Type with Dependence on the Gradient and the Laplacian. (2nd January 2018) - Ru, Yuanfang; Wang, Fanglei; Wang, Yunhai; An, Tianqing
Abstract : We consider a nonlocal fourth-order elliptic equation of Kirchhoff type with dependence on the gradient and LaplacianΔ 2 u - a + b ∫ Ω ∇ u 2 d x Δ u = f x, u, ∇ u, Δ u, inΩ, u = 0, Δ u = 0, on∂ Ω, wherea, b are positive constants. We will show that there existsb ⁎ > 0 such that the problem has a nontrivial solution for0 < b < b ⁎ through an iterative method based on the mountain pass lemma and truncation method developed by De Figueiredo et al., 2004.