arXiv Analytics

Sign in

arXiv:1401.1355 [math.AP]AbstractReferencesReviewsResources

A topological approach to the existence and multiplicity of positive solutions of $(p,q)$-Laplacian systems

Gennaro Infante, Mateusz Maciejewski, Radu Precup

Published 2014-01-07, updated 2014-01-24Version 2

In this paper we develop a new theory for the existence, localization and multiplicity of positive solutions for a class of non-variational,quasilinear, elliptic systems. In order to do this, we provide a fairly general abstract framework for the existence of fixed points of nonlinear operators acting on cones that satisfy an inequality of Harnack type. Our methodology relies on fixed point index theory. We also provide a non-existence result and an example to illustrate the theory.

Comments: 23 pages, 1 figure
Categories: math.AP
Subjects: 35J57, 35B09, 35B45, 35D30, 35J92, 47H10
Related articles: Most relevant | Search more
arXiv:1704.03194 [math.AP] (Published 2017-04-11)
On multiplicity of eigenvalues and symmetry of eigenfunctions of the $p$-Laplacian
arXiv:1802.07110 [math.AP] (Published 2018-02-20)
A priori bounds and multiplicity of positive solutions for $p$-Laplacian Neumann problems with sub-critical growth
arXiv:1312.6998 [math.AP] (Published 2013-12-25)
Multiplicity of Positive Solutions of P-Laplacian Systems With Sign-Changing Weight Functions

Links

Toolbox