Study of nonlinear elliptic problems of fourth order with critical exponents on compact Riemannian manifolds (Q1429974)

The author, using variational methods, proves existence theorems of solutions for the following elliptic partial differential equation of fourth-order with critical Sobolev exponent on a compact Riemannian manifold \(M\) of dimension \(n\) larger than \(4:\) \[ \triangle^2 \varphi + \nabla \left[a(x)\nabla \varphi\right ] + h(x) \varphi =\lambda f(x)\varphi | \varphi| ^{N-2} \] where \(a(x), h(x), f(x)\) are smooth functions on \(M,\) \(f(x)\) is positive and \(N=2n/(n -4).\) The author also proves a related result for a compact Riemannian manifold with boundary of dimension \(n >4\).