Normalized solutions to the Kirchhoff equation with $$L^2$$ L 2 -subcritical or critical nonlinearities in $${\varvec{\mathbb {R}}}^{2}$$ R 2

Jiaqing Hu () and Anmin Mao ()
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Jiaqing Hu: Qufu Normal University
Anmin Mao: Qufu Normal University

Indian Journal of Pure and Applied Mathematics, 2024, vol. 55, issue 2, 508-512

Abstract: Abstract In this paper, we study the existence of normalized solutions to the Kirchhoff equation with $$L^2$$ L 2 -subcritical or critical nonlinearities $$\begin{aligned} \begin{array}{ll} - \left( {a + b\int _{{\mathbb {R}}^{2}} {|\nabla u{|^2}dx} } \right) \Delta u = \lambda u + |u{|^{p - 2}}u + \mu |u{|^{q - 2}}u~~\textrm{in}~{\mathbb {R}}^{2}, \end{array} \end{aligned}$$ - a + b ∫ R 2 | ∇ u | 2 d x Δ u = λ u + | u | p - 2 u + μ | u | q - 2 u in R 2 , where $$a,b,\mu >0$$ a , b , μ > 0 , $$2

Keywords: Normalized solution; Kirchhoff equation; Minimizing method; 35J60; 35A15; 35B38 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s13226-023-00383-5

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