Multiple Solutions for Generalized Biharmonic Equations with Two Singular Terms

In this article, we investigate more general nonlinear biharmonic equation delta(2)u + V-lambda(x)u = mu f (x)u(-gamma) +g(x)u(p-1) in R-N,where delta(2) := delta(delta) is the biharmonic operator, N >= 1, lambda > 0 is a parameter, 0 < gamma < 1. Different from previous works on biharmonic problems, we suppose that V(x) = lambda a(x) - b(x) with lambda > 0 and b(x) could be singular at the origin. Under suitable conditions on V-lambda (x), f (x) and g(x), the multiplicity of solutions is obtained for lambda > 0 sufficiently large and some new estimates will be established. Our analysis is based on the Nehari manifold as well as the fibering map.