Ground states for a fractional scalar field problem with critical growth

الأصل · EN

We prove the existence of a ground state solution for the following fractional scalar field equation (-Δ)ˢ u= g(u) in Rⁿ where s∈ (0,1), N> 2s, (-Δ)ˢ is the fractional Laplacian, and g∈ C¹, β(R, R) is an odd function satisfying the critical growth assumption.