Entire solutions for critical \(p\)-fractional Hardy Schrödinger Kirchhoff equations. (English) Zbl 1423.35411

Piersanti, Paolo; Pucci, Patrizia

Publ. Mat., Barc. 62, No. 1, 3-36 (2018).

Through the mountain pass approach, the authors furnish sufficient conditions for having a nonzero solution for a critical \(p\)-fractional Hardy Schrödinger Kirchhoff equation (Theorems 1.1 and 1.3). The case of a general nonlocal integro-differential operator is also conducted (Theorem 4.1).

Reviewer: Mohammed El Aïdi (Bogotá)

MSC:

35R11	Fractional partial differential equations
35J60	Nonlinear elliptic equations
35J20	Variational methods for second-order elliptic equations
35B09	Positive solutions to PDEs

Keywords:

stationary Kirchhoff problems; nonlocal \(p\)-Laplacian operators; Hardy coefficients; critical exponents