A Generalization of Mahadevan′s Version of the Krein‐Rutman Theorem and Applications to p‐Laplacian Boundary Value Problems

Yujun Cui and Jingxian Sun

Abstract and Applied Analysis, 2012, vol. 2012, issue 1

Abstract: We will present a generalization of Mahadevan’s version of the Krein‐Rutman theorem for a compact, positively 1‐homogeneous operator on a Banach space having the properties of being increasing with respect to a cone P and such that there is a nonzero u ∈ P∖{θ} − P for which MTpu ≥ u for some positive constant M and some positive integer p. Moreover, we give some new results on the uniqueness of positive eigenvalue with positive eigenfunction and computation of the fixed point index. As applications, the existence of positive solutions for p‐Laplacian boundary‐value problems is considered under some conditions concerning the positive eigenvalues corresponding to the relevant positively 1‐homogeneous operators.

Date: 2012
References: Add references at CitEc
Citations:

Downloads: (external link)
https://doi.org/10.1155/2012/305279

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2012:y:2012:i:1:n:305279

Access Statistics for this article

More articles in Abstract and Applied Analysis from John Wiley & Sons
Bibliographic data for series maintained by Wiley Content Delivery ().