The effects of convolution and gradient dependence on a parametric Dirichlet problem

Dumitru Motreanu (), Calogero Vetro () and Francesca Vetro ()
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Dumitru Motreanu: University of Perpignan
Calogero Vetro: University of Palermo
Francesca Vetro: Ton Duc Thang University

Partial Differential Equations and Applications, 2020, vol. 1, issue 1, 1-15

Abstract: Abstract Our objective is to study a new type of Dirichlet boundary value problem consisting of a system of equations with parameters, where the reaction terms depend on both the solution and its gradient (i.e., they are convection terms) and incorporate the effects of convolutions. We present results on existence, uniqueness and dependence of solutions with respect to the parameters involving convolutions.

Keywords: Dirichlet problem; Convolution; System of elliptic equations; $$(p{; } q)$$ ( p; q ) -Laplacian; Parametric problems; 35J45; 35J55 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s42985-019-0004-y

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