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Tang, X. H.; Chen, Sitong
Calculus of variations and partial differential equations, 08/2017, Letnik: 56, Številka: 4Journal Article
This paper is dedicated to studying the following Kirchhoff-type problem 0.1 - a + b ∫ R 3 | ∇ u | 2 d x ▵ u + V ( x ) u = f ( u ) , x ∈ R 3 ; u ∈ H 1 ( R 3 ) , where a > 0 , b ≥ 0 are two constants, V ( x ) is differentiable and f ∈ C ( R , R ) . By introducing some new tricks, we prove that the above problem admits a ground state solution of Nehari–Pohozaev type and a least energy solution under some mild assumptions on V and f . Our results generalize and improve the ones in Guo (J Differ Equ 259:2884–2902, 2015 ) and Li and Ye (J Differ Equ 257:566–600, 2014 ) and some other related literature.
