Systems of Kirchhoff type equations with gradient dependence in the reaction term via subsolution-supersolution method

Elena Toscano; Calogero Vetro; Dariusz Wardowski

doi:10.3934/dcdss.2023070

Article Contents

2023, Volume 16, Issue 8: 2213-2229. Doi: 10.3934/dcdss.2023070

This issue Previous Article The radial bi-harmonic generalized Hartree equation revisited Next Article Preface

Systems of Kirchhoff type equations with gradient dependence in the reaction term via subsolution-supersolution method

1.
Department of Mathematics and Computer Science, University of PalermoVia Archirafi 34, 90123 Palermo, Italy
2.
Department of Nonlinear Analysis, Faculty of Mathematics and Computer Science, University of Lodz, Banacha 22, 90-238 Lodz, Poland

^*Corresponding author: Calogero Vetro
^*Corresponding author: Calogero Vetro

Received: September 2022

Revised: January 2023

Early access: April 3, 2023

Published online: April 3, 2023

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Abstract

We consider a Dirichlet problem for a system of equations involving Kirchhoff type $ p_i $-Laplacian differential operators and exhibiting gradient dependence in the reaction term (convection). Using the subsolution-supersolution method, we establish the existence of weak solutions into suitable ordered intervals. Following unified approach, we also provide a comparison argument to obtain positive solutions of certain models.

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Mathematics Subject Classification: Primary: 35J60; Secondary: 35J66.

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