Nehari-type ground state solutions for Kirchhoff type problems in ℝN. Issue 7 (19th May 2019)

• Record Type: Journal Article
• Authors: Cheng, Bitao; Li, Guofa; Tang, Xianhua
• Is Part Of: Applicable analysis. Volume 98:Issue 7(2019)
• Page Start: 1255
• Page End: 1266
• Publication Date: 2019-05-19
• Subjects: Kirchhoff-type problems -- Nehari-type ground state solutions -- non-Nehari manifold method; 35J20 -- 35J65; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2017.1419202
• Languages: English
• ISSNs: 0003-6811

Abstract

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.