Existence and non-existence results for a logistic-type equation on manifolds
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- by Stefano Pigola, Marco Rigoli and Alberto G. Setti PDF
- Trans. Amer. Math. Soc. 362 (2010), 1907-1936 Request permission
Abstract:
We study the steady state solutions of a generalized logistic-type equation on a complete Riemannian manifold. We provide sufficient conditions for existence, respectively non-existence of positive solutions, which depend on the relative size of the coefficients and their mutual interaction with the geometry of the manifold, which is mostly taken into account by means of conditions on the volume growth of geodesic balls.References
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Additional Information
- Stefano Pigola
- Affiliation: Dipartimento di Fisica e Matematica, Università dell’Insubria - Como, via Valleggio 11, I-22100 Como, Italy
- MR Author ID: 701188
- Email: stefano.pigola@uninsubria.it
- Marco Rigoli
- Affiliation: Dipartimento di Matematica, Università di Milano, via Saldini 50, I-20133 Milano, Italy
- MR Author ID: 148315
- Email: rigoli@mat.unimi.it
- Alberto G. Setti
- Affiliation: Dipartimento di Fisica e Matematica, Università dell’Insubria - Como, via Valleggio 11, I-22100 Como, Italy
- MR Author ID: 289546
- Email: alberto.setti@uninsubria.it
- Received by editor(s): February 17, 2006
- Received by editor(s) in revised form: September 7, 2007
- Published electronically: November 13, 2009
- © Copyright 2009
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 362 (2010), 1907-1936
- MSC (2000): Primary 58J05, 58J50; Secondary 35J60, 35P05, 53C21
- DOI: https://doi.org/10.1090/S0002-9947-09-04752-7
- MathSciNet review: 2574881
Dedicated: Dedicated to the memory of Franca Burrone Rigoli