ON THE GLOBAL BIFURCATION FOR A CLASS OF DEGENERATE EQUATIONS

We consider the nonlinear Dirichlet boundary value problems for the second order -(a(x)\u'(x)\p-2u'(x))' -lambdac(x)\u(x)\p-2u(x) = g(x, u(x), lambda), (a(x)\u''(x)\p-2u''(x))'' -lambdac(x)\u(x)\p-2u(x) = g(x, u(x), u, (x), lambda), with p greater-than-or-equal-to 2, a is-an-element-of C1, c is-an-element-of C, a, c > 0, g Caratheodory's function, and the partial differential -div (\delu\p-2delU) = lambda absolute value of p-2u + g(x, u(x), lambda) in OMEGA, u = 0 on partial derivative OMEGA, with p > 1, OMEGA c R(N) bounded domain. There is proved a global bifurcation result of Rabinowitz's type using the degree theoretical approach for the mappings acting from the Banach space X into its dual X*.