Critical second-order elliptic equation with zero Dirichlet boundary condition in four dimensions
Texas State University, Department of Mathematics
We are concerned with the nonlinear critical problem -∆u = K(x)u3, u > 0 in Ω, u = 0 on ∂Ω, where Ω is a bounded domain of ℝ4. Under the assumption that K is strictly decreasing in the outward normal direction on ∂Ω and degenerate at its critical points for an order β ∈ (1, 4), we provide a complete description of the lack of compactness of the associated variational problem and we prove an existence result of Bahri-Coron type.
Elliptic equation, Critical Sobolev exponent, Variational method, Critical point at infinity
Boucheche, Z., Chtioui, H., & Hajaiej, H. (2018). Critical second-order elliptic equation with zero Dirichlet boundary condition in four dimensions. <i>Electronic Journal of Differential Equations, 2018</i>(60), pp. 1-32.