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

Abstract

"Let $(M,g)$ be a Cartan-Hadamard manifold. For certain positive numbers $\mu$ and $\lambda$, we establish the multiplicity of solutions to the problem $$\Delta_g^2 u-\Delta_g u+u=\mu \frac{u}{d_g(x_0,x)^4}+\lambda \alpha(x)f(u),\ \mbox{ in } M,$$ where $x_0\in M$, while $f:\R\to\R$ is continuous function, superlinear at zero and sublinear at infinity."