Systems of quasilinear elliptic equations with dependence on the gradient via subsolution-supersolution method

Dumitru Motreanu; Calogero Vetro; Francesca Vetro

doi:10.3934/dcdss.2018017

Article Contents

2018, Volume 11, Issue 2: 309-321. Doi: 10.3934/dcdss.2018017

This issue Previous Article Location of Nodal solutions for quasilinear elliptic equations with gradient dependence Next Article Double resonance for Robin problems with indefinite and unbounded potential

Systems of quasilinear elliptic equations with dependence on the gradient via subsolution-supersolution method

1.
Department of Mathematics, University of Perpignan, 52, Avenue Paul Alduy, 66860 Perpignan, France
2.
Department of Mathematics and Computer Science, University of Palermo, Via Archirafi 34,90123 Palermo, Italy
3.
Department of Energy, Information Engineering and Mathematical Models, University of Palermo, Viale delle Scienze, 90128 Palermo, Italy

Received: February 2017

Revised: May 2017

Published: April 2018

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Abstract

For the homogeneous Dirichlet problem involving a system of equations driven by $(p,q)$-Laplacian operators and general gradient dependence we prove the existence of solutions in the ordered rectangle determined by a subsolution-supersolution. This extends the preceding results based on the method of subsolution-supersolution for systems of elliptic equations. Positive and negative solutions are obtained.

Keywords:

Dirichlet problem,
system of elliptic equations,
$(p,
q)$-Laplacian,
subsolution-supersolution and gradient dependence.

Mathematics Subject Classification: Primary: 35J92; Secondary: 35J57.

Citation:

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References

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