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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

Marta García-Huidobro 1, , Raul Manásevich 2, and  J. R. Ward 3,

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.
Keywords: bifurcation, Asymptotically homogeneous operators, nonlinear boundary value problems, p-Laplacian systems, pseudo-eigenvalue..
Mathematics Subject Classification: 34A34, 34B15, 34C23, 47J05, 47H11, 47J10, 47J1.
Citation: Marta García-Huidobro, Raul Manásevich, J. R. Ward. Vector p-Laplacian like operators, pseudo-eigenvalues, and bifurcation. Discrete & Continuous Dynamical Systems, 2007, 19 (2) : 299-321. doi: 10.3934/dcds.2007.19.299
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