On the principal eigenvalue of degenerate quasilinear elliptic systems
- 13 August 2008
- journal article
- research article
- Published by Wiley in Mathematische Nachrichten
- Vol. 281 (9) , 1351-1365
- https://doi.org/10.1002/mana.200510683
Abstract
We study the properties of the positive principal eigenvalue of a degenerate quasilinear elliptic system. We prove that this eigenvalue is simple, unique up to positive eigenfunctions and isolated. Under certain restrictions on the given data, the regularity of the corresponding eigenfunctions is established. The extension of the main result in the case of an unbounded domain is also discussed.Keywords
This publication has 36 references indexed in Scilit:
- Global bifurcation results on degenerate quasilinear elliptic systemsNonlinear Analysis, 2007
- Estimates for eigenvalues of quasilinear elliptic systemsJournal of Differential Equations, 2006
- An optimization problem for the first eigenvalue of the $p-$Laplacian plus a potentialCommunications on Pure & Applied Analysis, 2006
- Global solutions for quasilinear parabolic systemsJournal of Differential Equations, 2004
- Global existence of solutions of a strongly coupled quasilinear parabolic system with applications to electrochemistryJournal of Differential Equations, 2003
- Estimates for elliptic systems from composite materialCommunications on Pure and Applied Mathematics, 2003
- Existence of multiple solutions for quasilinear systems via fibering methodJournal of Differential Equations, 2003
- Effects of Certain Degeneracies in the Predator-Prey ModelSIAM Journal on Mathematical Analysis, 2002
- Harnack's inequality for cooperative weakly coupled elliptic systemsCommunications in Partial Differential Equations, 1999
- On the Equation div( | ∇u | p-2 ∇u) + λ | u | p-2 u = 0Proceedings of the American Mathematical Society, 1990