A result on a non-autonomous Kirchhoff type equation involving critical term. (November 2018) - Liu, Jiu; Liu, Tao; Pan, Hui-Lan
Abstract: By using the method of Nehari manifold, we obtain the existence of a positive ground state solution for the following non-autonomous Kirchhoff type equation − ( a + b ∫ R N | ∇ u | 2 d x ) △ u + V ( x ) u = u N + 2 N − 2, x ∈ R N, u ∈ D 1, 2 ( R N ), N = 3, 4, where a > 0, b > 0 and V satisfies some appropriate assumptions.