Abstract
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.
Authors
Radu Precup
Department of Mathematics Babes-Bolyai University, Cluj-Napoca, Romania
Keywords
weak Harnack inequality; fixed point index; p-Laplace operator; quasilinear elliptic system; positive weak solution; cone; multiplicity; nonexistence
Paper coordinates
G. Infante, M. Maciejewski, R. Precup, A topological approach to the existence and multiplicity of positive solutions of (p,q)-Laplacian systems, Dyn. Partial Differ. Equ. 12 (2015), no.3, 193-215, http://dx.doi.org/10.4310/DPDE.2015.v12.n3.a1
About this paper
Journal
Dynamics of Partial Differential Equations
Publisher Name
Print ISSN
1548159X
Online ISSN
21637873
google scholar link
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