EXISTENCE OF RADIAL SIGN-CHANGING SOLUTIONS FOR FRACTIONAL KIRCHHOFF-TYPE PROBLEMS IN R3

In this paper, the following fractional Kirchhoff-type problem ( a + b integral(R3) broken vertical bar(-Delta)(s/2) u broken vertical bar(2)dx)(-Delta)(s)u + V(x)u = f (x, u), x is an element of R-3, where a, b > 0 are constants, s is an element of ( 3/4, 1), 2(s)* = 6/3-2s, V: R-3 -> R is a continuous function, and f : R-3 x R -> R is a continuous function, is considered. It is demonstrated that the fractional Kirchhoff-type equation has a radial sign-changing solution u(b) and a radial solution (u) over bar (b) when f does not satisfy the subcritical growth condition and the usual Nehari-type monotonicity condition. The main tools are the constraint variational method and some analysis techniques.