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The aim of this article is twofold: firstly, we deal with the existence and multiplicity of weak solutions to the Kirchhoff problem:where Ω is a smooth bounded domain inand. Secondly, we deal with the existence and multiplicity of weak solutions to the Kirchhoff problem:whereand. We assume that  f  and  g  have critical exponential growth at infinity. To establish our existence results, we use the mountain pass theorem, Ekeland variational principle and Moser–Trudinger inequality.

Existence and multiplicity of solutions to N -Kirchhoff equations with critical exponential growth and a perturbation term