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

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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.

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Correspondence to Dumitru Motreanu.

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Motreanu, D., Vetro, C. & Vetro, F. The effects of convolution and gradient dependence on a parametric Dirichlet problem. SN Partial Differ. Equ. Appl. 1, 3 (2020) doi:10.1007/s42985-019-0004-y

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Keywords

  • Dirichlet problem
  • Convolution
  • System of elliptic equations
  • \((p{, } q)\)-Laplacian
  • Parametric problems

Mathematics Subject Classification

  • 35J45
  • 35J55