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Discontinuity, Nonlinearity, and Complexity 13(4) (2024) 621--632 | DOI:10.5890/DNC.2024.12.004

Soukaina Yacini, Chakir Allalou, Khalid Hilal

Laboratory LMACS, FST of Beni Mellal, Sultan Moulay Slimane University, Morocco

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Abstract

In the present paper, we investigate the existence of at least one weak solution to the Dirichlet boundary value problem involving the $p(x)$-Kirchhoff type equation with a reaction term depending also on the gradient (convection). Our result is obtained by means of the theory of topological degree and the theory of variable exponent Sobolev spaces.

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