A Generalization of Mahadevan's Version of the Krein-Rutman Theorem and Applications to p-Laplacian Boundary Value Problems
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 co...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2012-01-01
|
| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2012/305279 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | 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. |
|---|---|
| ISSN: | 1085-3375 1687-0409 |