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Title: | Existence and multiplicity of solutions to N-Kirchhoff equations with critical exponential growth and a perturbation term |
Authors: | Dwivedi, Gaurav |
Keywords: | Mathematics Kirchhoff type problem Exponential nonlinearity Variational methods Critical growth |
Issue Date: | Mar-2022 |
Publisher: | Taylor & Francis |
Abstract: | The aim of this article is twofold: firstly, we deal with the existence and multiplicity of weak solutions to the Kirchhoff problem: ⎧ ⎪ ⎨ ⎪ ⎩ −𝑎(∫Ω|∇𝑢|𝑁d𝑥)Δ𝑁𝑢= 𝑓(𝑥,𝑢) |𝑥|𝑏 +𝜆ℎ(𝑥)in Ω,𝑢=0on ∂Ω, where Ω is a smooth bounded domain in ℝ𝑁(𝑁≥ 2) and 0≤𝑏<𝑁. Secondly, we deal with the existence and multiplicity of weak solutions to the Kirchhoff problem: −𝑎(∫ℝ𝑁|∇𝑢|𝑁+𝑉(𝑥)|𝑢|𝑁d𝑥)(Δ𝑁𝑢+𝑉(𝑥)|𝑢|𝑁−2𝑢)= 𝑔(𝑥,𝑢) |𝑥|𝑏 +𝜆ℎ(𝑥)in ℝ𝑁, where 𝑁≥ 2 and 0≤𝑏<𝑁. 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. |
URI: | https://www.tandfonline.com/doi/full/10.1080/17476933.2022.2048297 http://dspace.bits-pilani.ac.in:8080/jspui/handle/123456789/17361 |
Appears in Collections: | Department of Mathematics |
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