Weak solutions for a fractional p-Laplacian equation with sign-changing potential

作者：Xu, Jiafa^*; Wei, Zhongli; Dong, Wei

来源：Complex Variables and Elliptic Equations, 2016, 61(2): 284-296.

DOI：10.1080/17476933.2015.1076808

• fractional p-Laplacian
• critical point theorems
• weak solution

In this paper, we use some critical point theorems to discuss the existence of weak solutions for the fractional p-Laplacian equation in R-N @@@ (-Delta)(p)(alpha)u + V(x) vertical bar u vertical bar(p-2)u - lambda vertical bar u vertical bar(p-2)u = f(x, u) + g(x) vertical bar u vertical bar(q-2)u, x is an element of R-N. @@@ where N, p >= 2, alpha is an element of ( 0, 1), lambda is a parameter, (-Delta)(p)(alpha) is the fractional p-Laplacian and f : R-N x R -> R is a Caratheodory function.

• 出版日期2016-2-1
• 单位河北工程大学; 重庆师范大学; 山东建筑大学