Critical stationary Kirchhoff equations in RN involving nonlocal operators

Lately Fiscella and Valdinoci in [A critical Kirchhoff type problem involving a nonlocal operator, Nonlinear Anal. 94 (2014), 156-170] proposed a stationary Kirchhoff variational model, in bounded regular domains of RN, which takes into account the nonlocal aspect of the tension arising from nonlocal measurements of the fractional length of the string. In this talk, inspired by the above paper and by recent results of the speaker, we extend in several directions the above paper in the entire RN.