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Please use this identifier to cite or link to this item: http://dspace.bits-pilani.ac.in:8080/jspui/handle/123456789/17361
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)⁢Δ𝑁⁢𝑢= 𝑓⁡(𝑥,𝑢) |𝑥|𝑏 +𝜆⁢ℎ⁡(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)⁢(Δ𝑁⁢𝑢+𝑉⁡(𝑥)⁢|𝑢|𝑁−2⁢𝑢)= 𝑔⁡(𝑥,𝑢) |𝑥|𝑏 +𝜆⁢ℎ⁡(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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