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

Marta García-Huidobro; Raul Manásevich; J. R. Ward

doi:10.3934/dcds.2007.19.299

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2007, Volume 19, Issue 2: 299-321. Doi: 10.3934/dcds.2007.19.299

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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

Received: October 31, 2005

Revised: October 31, 2006

Published: April 2007

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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 nontrivial solutions is studied. Conditions for bifurcation, from either zero or infinity, at the pseudo-eigenvalues are given.

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Mathematics Subject Classification: 34A34, 34B15, 34C23, 47J05, 47H11, 47J10, 47J15.

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