Existence and Multiplicity Results for Fractional Schrodinger Equation with Critical Growth

摘要

This paper deals with the following fractional Schrodinger equation with critical growth @@@ {(-Delta)(s)u + V(x)u = vertical bar u vertical bar(2s)*(-2)u, x is an element of Omega, @@@ u = 0, x is an element of R-N\Omega, @@@ where Omega = R-N or Omega is an open bounded domain of R-N , N > 2s with s is an element of (0, 1) and V (x) is a sign-changing function. Firstly, using a nonlocal version of the second concentration-compactness principle, we prove the existence of Mountain-Pass solution for the above equation in R-N. Secondly, we prove the existence of N distinct pairs of nontrivial solutions for the above equation in R-N by using a global compactness result and Krasnoselskii's genus theory, as well as in bounded domains.

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