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


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.


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


weak Harnack inequality; fixed point index; p-Laplace operator; quasilinear elliptic system; positive weak solution; cone; multiplicity; nonexistence

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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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Dynamics of Partial Differential Equations

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