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

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

Gennaro Infante
Dipartimento di Matematica ed Informatica, Università della Calabria, Cosenza, Italy

Mateusz Maciejewski
Faculty of Mathematics and Computer Science, Nicolaus Copernicus UniversityToruń, Poland

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

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About this paper

Journal

Dynamics of Partial Differential Equations

Publisher Name
Print ISSN

1548159X

Online ISSN

21637873

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