# American Institute of Mathematical Sciences

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May  2007, 19(2): 299-321. doi: 10.3934/dcds.2007.19.299

## Vector p-Laplacian like operators, pseudo-eigenvalues, and bifurcation

 1 Department of Mathematics, Pontificia Universidad Católica de Chile, Casilla 306, Correo 22, Santiago 2 Centro de Modelamiento Matemático and Departamento de Ingenieria Matemática, F.C.F.M, Universidad de Chile, Casilla 170, Correo 3, Santiago 3 Department of Mathematics, University of Alabama at Birmingham, Birmingham, AL, 35294-1170, United States

Received  November 2005 Revised  November 2006 Published  July 2007

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 nontrivial solutions is studied. Conditions for bifurcation, from either zero or infinity, at the pseudo-eigenvalues are given.
Citation: Marta García-Huidobro, Raul Manásevich, J. R. Ward. Vector p-Laplacian like operators, pseudo-eigenvalues, and bifurcation. Discrete & Continuous Dynamical Systems - A, 2007, 19 (2) : 299-321. doi: 10.3934/dcds.2007.19.299
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