Radial solutions for a fractional Kirchhoff type equation in $$\mathbb {R}^N$$ R N

Mohammed Massar () and Mohamed Talbi ()
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Mohammed Massar: FTSH, Abdelmalek Essaadi University
Mohamed Talbi: CRMEF

Indian Journal of Pure and Applied Mathematics, 2021, vol. 52, issue 3, 897-902

Abstract: Abstract This work is concerned with the following equation of Kirchhoff type involving the fractional Laplacian $$\begin{aligned} \left( a+b\int _{\mathbb {R}^N}\left| (-\varDelta )^{\frac{s}{2}}u\right| ^2dx\right) (-\varDelta )^su+u=f(u) \, \text{ in } \mathbb {R}^N. \end{aligned}$$ a + b ∫ R N ( - Δ ) s 2 u 2 d x ( - Δ ) s u + u = f ( u ) in R N . By transforming this equation into an equivalent system, under suitable assumptions we establish the existence of at least two nontrivial radial solutions without (AR) condition. Moreover, the nonexistence of solutions is also investigated.

Keywords: Fractional Kirchhoff equations; Radial solutions; Variational methods; 35A15; 35J60; 35R09 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s13226-021-00106-8

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