A Class Of P-laplace Equation Solution Problem

In this paper, by constructing suitable truncations, we use variational method, upper-lower solution theory and critical point theory to study existence of the biggest solution and multiple solutions for the p-Laplacian equationWhereλis a positive parameter,Ω(?) R^N is a bounded domain with C² boundary (?) andâ–³_pu = div(?) is the p-Laplacian operator. We assume 1＜p＜τ₁＜τ₂＜p^*, p^* denotes the critical Sobolev exponent, i.e.