Two positive solutions of a quasilinear elliptic Dirichlet problem (Q640729)

For a classs of second order quasilinear elliptic equations the author establishes the existence of two nonnegative weak solutions of the Dirichlet problem on a bounded domain \(\Omega \subset R^n. \) Solutions of the boundary value problem are critical points of the \(C^1\)-functional on the Sobolev space \(H^1_0(\Omega)\). One solution, \(u_1, \) is a strict local minimum whereas the other, \(u_2, \) is characterized by a minimax principle of mountain pass type. Furthermore, the author shows that \(u_1 \) is not a global minimum.