MOUNTAIN PASS SOLUTIONS FOR THE FRACTIONAL BERESTYCKI-LIONS PROBLEM

作者：Ambrosio Vincenzo^*

来源：Advances in Differential Equations, 2018, 23(5-6): 455-488.

We investigate the existence of least energy solutions and infinitely many solutions for the following nonlinear fractional equation
(-Delta)(s)u = g(u) in R-N,
where s is an element of (0,1), N >= 2, (-Delta)(s) is the fractional Laplacian and g : R -> R is an odd C-1,C-alpha function satisfying Berestycki-Lions type assumptions. The proof is based on the symmetric mountain pass approach developed by Hirata, Ikoma and Tanaka in [33]. Moreover, by combining the mountain pass approach and an approximation argument, we also prove the existence of a positive radially symmetric solution for the above problem when g satisfies suitable growth conditions which make our problem fall in the so called "zero mass" case.

• 出版日期2018-6