Biharmonic Equations Involving Concave-Convex Nonlinearities and Multiple Singular Potentials

In this project, we will investigate the following biharmonic equation (E_λ) involving concave-convex nonlinearities and multiple singular potentials \Delta^2 u-\sum_{i=1}^{k}\frac{\mu_{i}}{|x-a_i|^4}u=|u|^{2*-2}u+λ|u|^{q-2}u in Ω, u=\frac{\partial u}{\partial n}=0, on \partial Ω,where Ω is a smooth bounded domain in R^N (N \ge 5) such that the points a_i \in Ω, i=1,2,...,k, k\ge 2, are different, 0\le μ_i＜ \bar{μ} =((N(N-4))/4)^2, 1＜q＜2, 2*=(2N)/(N-4) denotes the critical Sobolev exponent, and λ ＞ 0 is a parameter. We will hope to obtain the existence and multiplicity results of positive solutions to the equation (E_λ) when the parameters λ, q and μ_i, (i = 1,2,...,k) satisfy some suitable hypothesis.

Project ID:PA10708-1086
External Project ID:MOST107-2115-M182-002