A BIFURCATION RESULT FOR EQUATIONS WITH ANISOTROPIC p-LAPLACE-LIKE OPERATORS

where X is an appropriate function space and φi , F are given functions. The coefficients φi’s are different in general. In the particular case where φi(|ξ |)= |ξ |p−2, for all ξ ∈ R , for all i ∈ {1, . . . ,N}, (1.1) reduces to the p-Laplacian equation and there are several bifurcation results available (cf. [3, 4]). It seems that bifurcation problems for anisotropic elliptic operators have not been addressed in detail. As is well known in bifurcation theory, a first step is to find a “linearization” of (1.1) such that bifurcation in (1.1) can be studied through the eigenvalues and eigenfunctions of the linearization. Different from equations with compact perturbations of linear operators, we show that (1.1) can be related to a nonlinear but homogeneous equation (called the homogenization of (1.1)). Another difficulty is that since the functions φi’s may have different growths at