Multiple solution for a fourth-order nonlinear eigenvalue problem with singular and sublinear potential

摘要

Let (M, g) be a Cartan-Hadamard manifold. For certain positive num-bers mu and lambda, we establish the multiplicity of solutions to the problem Delta 2gu - Delta gu + u = mu u dg(x0, x)4 + lambda alpha(x)f (u), in M, where x0 is an element of M, while f : R -> R is continuous function, superlinear at zero and sublinear at infinity.