A result on a non-autonomous Kirchhoff type equation involving critical term. (November 2018)

• Record Type: Journal Article
• Authors: Liu, Jiu; Liu, Tao; Pan, Hui-Lan
• Is Part Of: Applied mathematics letters. Volume 85(2018)
• Page Start: 82
• Page End: 87
• Publication Date: 2018-11
• Subjects: Kirchhoff type equation -- Nehari manifold -- Positive solution; Applied mathematics -- Periodicals; 519.05
• DOI: 10.1016/j.aml.2018.05.026
• Languages: English
• ISSNs: 0893-9659

Abstract

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.