Existence of Solutions for a Fractional Laplacian Equation with Critical Nonlinearity

الملخص EN

We study the fractional Laplacian equation (−Δ)su+λA(x)u=μu+|u|2*(s)-2u, x∈ℝN, here N>2s, s∈(0,1), 2*(s)=2N/(N-2s) is the critical exponent, and A(x)≥0 is a real potential function.

Employing the variational method we prove the existence of nontrivial solutions for μ small and λ large.