Nehari-type ground state solutions for asymptotically periodic fractional Kirchhoff-type problems in RN

作者：Peng, Jiawu^*; Tang, Xianhua; Chen, Sitong

来源：Boundary Value Problems, 2018, 2018(1): 3.

DOI：10.1186/s13661-017-0922-6

• fractional Kirchhoff-type problem
• Nehari-type ground state solution
• asymptotically periodic
• asymptotically cubic and super-cubic growth

In this paper, we studied the following fractional Kirchhoff-type equation: @@@ (a + b integral(RN) vertical bar(-Delta)(alpha/2)u vertical bar(2) dx)(-Delta)(alpha)u +V(x)u = f(x, u), x is an element of R-N, @@@ where a, b are positive constants, alpha is an element of (0, 1), N is an element of (2 alpha, 4 alpha), (-Delta)(alpha) is the fractional Laplacian operator, V(x) and f(x, u) are periodic or asymptotically periodic in x. Under some weaker conditions on the nonlinearity, we obtain the existence of ground state solutions for the above problem in periodic case and asymptotically periodic case, respectively. In particular, our results unify both asymptotically cubic and super-cubic nonlinearities, which are new even for alpha = 1.

• 出版日期2018-1-5
• 单位中南大学