D. Applebaum, Lévy Processes and Stochastic Calculus, Cambridge University Press, Cambridge, 2004.

A. Arosio and S. Panizzi, On the well-posedness of the Kirchhoff string, Trans. Amer. Math. Soc. 348 (1996), 305–350.

B. Barrios, E. Colorado, A. de Pablo and U. Sánchez, On some critical problems for the fractional Laplacian operator, J. Differential Equations 252 (2012), 6133–6162.

B. Barrios, L.M. Del Pezzo, J. Garcı́a-Melián and A. Quaas, A priori bounds and existence of solutions for some nonlocal elliptic problems, Mathematics 34 (2018), 195–220.

J. Bertoin, Lévy Processes, Cambridge University Press, Cambridge, 1998.

J.P. Bouchaud and A. Georges, Anomalous diffusion in disordered media. Statistical mechanics, models and physical applications, Phys. Rep. 195 (1990), 127–293.

C. Brändle, E. Colorado, A. de Pablo, U. Sánchez, A concave-convex elliptic problem involving the fractional Laplacian, Proc. Roy. Soc. Edinburgh 143 (2013), 39–71.

L. Caffarelli, Further regularity for the Signorini problem, Comm. Partial Differential Equations 4 (1979), 1067–1075.

L. Caffarelli and L. Silvestre, An extension problem related to the fractional Laplacian, Comm. Partial Differential Equations 32 (2007), 1245–1260.

K. Chang, Methods of Nonlinear Analysis, Monographs in Mathematics, Springer–Verlag, Berlin, 2005.

W. Chen, W. Dai and G. Qin, Liouville type theorems, a priori estimates and existence of solutions for critical and super-critical order Hardy–Hénon type equations in Rn , arXiv:1808.06609, 36 pp.

W. Chen, Y. Fang and R. Yang, Liouville theorems involving the fractional Laplacian on a half space, Adv. Math. 274 (2015), 167–198.

W. Chen and C. Li, Regularity of solutions for a system of integral equations, Comm. Pure Appl. Anal. 4 (2005), 1–8.

W. Chen, C. Li and Y. Li, A direct blowing-up and rescaling argument on nonlocal elliptic equations, Internat. J. Math. 27 (2016), 1650064.

W. Chen, C. Li and Y. Li, A direct method of moving planes for the fractional Laplacian, Adv. Math. 308 (2017), 404–437.

W. Chen, C. Li and B. Ou, Classification of solutions for an integral equation, Comm. Pure Appl. Math. 59 (2006), 330–343.

W. Chen and J. Zhu, Indefinite fractional elliptic problem and Liouville theorems, J. Differential Equations 260 (2016), 2758–2785.

Q. Dai, E. Lan and F. Shi, A priori bounds for positive solutions of Kirchhoff type equations, Comput. Math. Appl. 76 (2018), 1525–1534.

W. Dai and G. Qin, Liouville type theorems fractional and higher order Hénon–Hardy type equations via the method of scaling spheres, Int. Math. Res. Not. IMRN, 70 pp., DOI:10.1093/imrn/rnac079.

D. de Figueiredo and J. Yang, A priori bounds for positive solutions of a nonvariational elliptic system, Comm. Partial Differential Equations 26 (2001), 2305–2321.

A. Fiscella and P. Mishra, The Nehari manifold for fractional Kirchhoff problems involving singular and critical terms, Nonlinear Anal. 186 (2019), 6–32.

A. Fiscella and E. Valdinoci, A critical Kirchhoff type problem involving a nonlocal operator, Nonlinear Anal. 94 (2014), 156–170.

B. Gidas and J. Spruck, A priori bounds for positive solutions of nonlinear elliptic equations, Comm. Partial Differential Equations 6 (1981), 883–901.

Q. Guan, Integration by parts formula for regional fractional Laplacian, Comm. Math. Phys. 266 (2006), 289–329.

H. Jin and W. Liu, Fractional Kirchhoff equation with a general critical nonlinearity, Appl. Math. Lett. 74 (2017), 140–146.

P. Mishra and K. Sreenadh, Existence and multiplicity results for fractional p-Kirchhoff equation with sign changing nonlinearities, Adv. Pure Appl. Math. 7 (2016), 97–114.

L. Zhang, M. Yu and J. He, A Liouville theorem for a class of fractional systems in Rn+, J. Differential Equations 263 (2017), 6025–6065.