Nehari-type ground state solutions for Kirchhoff type problems in ℝN. Issue 7 (19th May 2019) - Cheng, Bitao; Li, Guofa; Tang, Xianhua
ABSTRACT: In the present paper, by employing Non-Nehari manifold method, we make use of a weak condition on the existence of Nehari-type ground state solutions for the following Kirchhoff-type problem (0.1) - a + b ∫ R N | ∇ u | 2 d x ▵ u + V ( x ) u = f ( x, u ), x ∈ R N ; u ∈ H 1 ( R N ), which weakens both the variant Ambrosetti–Rabinowitz condition and the variant Nehari-type condition related to Problem (0.1). Furthermore, we allowf ( x, u ) u - 4 F ( x, u ) to be sign-changing, which is different from the previous literature.