Bounded domain 2 Critical Sobolev exponent 2 Critical growth 2 Dirichlet boundary condition 2 Laplace equation 2 Laplace transforms 2 Mathematical operators 2 Multiple solutions 2 Nonlinear equations 2 Nontrivial solution 2 P-Laplace equations P-Laplace operator 2 P-Laplacian 2 Quasilinear elliptic equations 2 Variational methods 2 p-Laplace equations 2