A bifurcation problem or a nonlinear eigenvalue problem for degenerate quasilinear elliptic equations with Dirichlet boundary condition is studied. Uniform estimates of partial derivatives of solutions are calculated. By virtue of these estimatates, we can apply the Leray-Schauder degree theory to our problem and obtain the bifurcation of nontrivial weak solutions.
"A bifurcation problem of some nonlinear degenerate elliptic equations." Adv. Differential Equations 2 (6) 895 - 926, 1997.