Multiple solutions for pp-harmonic type equations

In this paper, we establish the existence of multiple solutions for an equation involving a pp-harmonic operator, subject to Dirichlet boundary conditions in a bounded smooth open domain of RNRN, while the nonlinearity has a (p−1)(p−1)-sublinear growth at infinity. Using a three critical points theorem, we prove the existence of at least three distinct weak solutions in W02,p(Ω) to this problem.