Multiplicity and concentration of solutions for fractional Schrodinger equation with sublinear perturbation and steep potential well

作者：Yang, Liu; Liu, Zhisu^*

来源：Computers & Mathematics with Applications, 2016, 72(6): 1629-1640.

DOI：10.1016/j.camwa.2016.07.033

• Fractional Laplacian
• Variational method
• Multiplicity
• Concentration

this paper, we investigate the following fractional Schrodinger equation with sublinear perturbation and steep potential well @@@ {(-Delta)(s)u + lambda V (x)u = f (x, u) + alpha(x) vertical bar u vertical bar v(-2)u in R-N, @@@ {u is an element of H-s (R-N), @@@ where 0 < s < 1, 2s < N, lambda > 0, 1 < v < 2,f is an element of C (R-N x R) is of subcritical growth. By using variational methods, we prove that such a class of equations possess at least two nontrivial solutions. Moreover, the phenomenon of concentration of solutions is explored as well.

• 出版日期2016-9
• 单位衡阳师范学院; 湖南大学; 南华大学