Existence and multiplicity of solutions for a singular problem involving the p-biharmonic operator in RN

In this paper, we are interested in the existence and the multiplicity of solutions for the following singular p-biharmonic problem with Rellich potential Delta(2)(p)u - mu vertical bar u vertical bar(p-2)u/vertical bar x vertical bar(2p) - Delta(p)u = lambda f(x)u(q-1) + g(x)u(m-1), in R-N u(x) > 0, in R-N where 1 < p < N/2, 0 < m < 1, p < q < pN/N - 2p, lambda is a positive real parameter and 0 < mu < gamma(N,p) with gamma(N,p) = (N(p-1) (N-2p)/p(2))(p). Under some appropriate assumptions on the functions f and g, by using the Nehari manifold combined with the fibering maps, we obtain the existence of two positive entire solutions. (C) 2021 Published by Elsevier Inc.