Differential and Integral Equations
- Differential Integral Equations
- Volume 24, Number 11/12 (2011), 1107-1124.
Principal eigenvalue for quasilinear cooperative elliptic systems
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  and Dancer . 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  for the scalar case.
Differential Integral Equations, Volume 24, Number 11/12 (2011), 1107-1124.
First available in Project Euclid: 20 December 2012
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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