Three solutions for a fractional p-Laplacian problem

We deal with the following fractional p-Laplacian problem {(-Delta)(p)(s) u = lambda f (x, u) in Omega, u = 0 in Omega(c), where Omega subset of R-N (N >= 2) is a bounded domain with C-1,C- 1 boundary, s is an element of (0, 1), 2 <= p < N/s, (-Delta)(p)(s) is the fractional p-Laplacian and f : Omega x R -> R is a Caratheodary function having (p - 1)-sublinear growth near zero. By using variational arguments and Morse theory, for lambda > 0 small enough we obtain three nontrivial solutions: two of them are fixed sign, the other one is nodal.

Automated summary

This article deals with a fractional p-Laplacian problem on a bounded domain Omega, and using variational arguments and Morse theory, three nontrivial solutions are obtained.