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EIGENVALUE HOMOGENISATION PROBLEM WITH INDEFINITE WEIGHTS

Part of: Partial differential equations Spectral theory and eigenvalue problems

Published online by Cambridge University Press:  15 October 2015

JULIÁN FERNÁNDEZ BONDER ,
JUAN P. PINASCO  and
ARIEL M. SALORT
JULIÁN FERNÁNDEZ BONDER*
Affiliation:
Departamento de Matemática, IMAS – CONICET, FCEyN – Universidad de Buenos Aires, Ciudad Universitaria, Pabellón I, (1428) Av. Cantilo s/n., Buenos Aires, Argentina email jfbonder@dm.uba.ar
JUAN P. PINASCO
Affiliation:
Departamento de Matemática, IMAS – CONICET, FCEyN – Universidad de Buenos Aires, Ciudad Universitaria, Pabellón I, (1428) Av. Cantilo s/n., Buenos Aires, Argentina email jpinasco@dm.uba.ar
ARIEL M. SALORT
Affiliation:
Departamento de Matemática, IMAS – CONICET, FCEyN – Universidad de Buenos Aires, Ciudad Universitaria, Pabellón I, (1428) Av. Cantilo s/n., Buenos Aires, Argentina email asalort@dm.uba.ar
*
✉jfbonder@dm.uba.ar
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Abstract

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In this work we study the homogenisation problem for nonlinear elliptic equations involving $p$-Laplacian-type operators with sign-changing weights. We study the asymptotic behaviour of variational eigenvalues which consist of a double sequence of eigenvalues. We show that the $k$th positive eigenvalue goes to infinity when the average of the weights is nonpositive, and converges to the $k$th variational eigenvalue of the limit problem when the average is positive for any $k\geq 1$.

Keywords

p-Laplace-type problemseigenvalueshomogenisationindefinite weights

MSC classification

Primary: 35B27: Homogenization; equations in media with periodic structure
Secondary: 35P15: Estimation of eigenvalues, upper and lower bounds 35P30: Nonlinear eigenvalue problems, nonlinear spectral theory
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 93 , Issue 1 , February 2016 , pp. 113 - 127
Copyright
© 2015 Australian Mathematical Publishing Association Inc. 

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