Differential and Integral Equations

Principal eigenvalue for quasilinear cooperative elliptic systems

Liamidi Leadi and Humberto Ramos Quoirin

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We study the first eigenvalue of a $\lambda$-dependent cooperative elliptic system involving two quasilinear operators. By variational arguments, we find an expression for the limit of this eigenvalue as $\lambda \rightarrow -\infty$, which improves and extends (for gradient quasilinear systems) a result proved by Álvarez Caudevilla-López Gómez [4] and Dancer [9]. We apply this result to deduce the existence of strictly principal eigenvalues (i.e., whose eigenfunctions have both components positive) of a weighted system and extend the results proved in Cuesta-Ramos Quoirin [7] for the scalar case.

Article information

Differential Integral Equations, Volume 24, Number 11/12 (2011), 1107-1124.

First available in Project Euclid: 20 December 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35J 35P30: Nonlinear eigenvalue problems, nonlinear spectral theory 35J50: Variational methods for elliptic systems


Leadi, Liamidi; Quoirin, Humberto Ramos. Principal eigenvalue for quasilinear cooperative elliptic systems. Differential Integral Equations 24 (2011), no. 11/12, 1107--1124. https://projecteuclid.org/euclid.die/1356012879

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