Vector p-laplacian like operators, pseudo-eigenvalues, and bifurcation

Abstract

Boundary value problems for systems of ordinary differential equations are studied. These systems involve asymptotically homogeneous operators. Leray-Schauder indices are calculated for these operators and the concept of pseudo-eigenvalue is defined. The existence of nontrival solutions is studied. Conditions for bifurcation, from either zero or infinity, at the pseudo-eigenvalues are given.