In this paper we develop a new theory for the existence, local- ization 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.

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

INFANTE, GENNARO
;
2015

Abstract

In this paper we develop a new theory for the existence, local- ization 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.
Weak Harnack inequality, fixed point index, p-Laplace operator, quasilinear elliptic system, positive weak solution, cone, multiplicity, nonexistence.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11770/153953
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