Multiple positive solutions for a fractional Kirchhoff type equation with logarithmic and singular nonlinearities

Lei, Jun (2023) Multiple positive solutions for a fractional Kirchhoff type equation with logarithmic and singular nonlinearities. ELECTRONIC JOURNAL OF QUALITATIVE THEORY OF DIFFERENTIAL EQUATIONS, 2023 (53). pp. 1-16. ISSN 1417-3875

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Abstract

In this paper, we study the following fractional Kirchhoff type equation a +b u >0, u =0, RN RN |u(x) −u(y)|p |x −y|N+ps dxdy (−∆)s pu = |u|q−2uln|u|2 + λ uγ, in Ω, in Ω, in RN\Ω, where Ω ⊂ RN is a bounded domain with Lipschitz boundary, 0 < s < 1 < p, 0 < γ <1, a > 0,b ≥ 0, N > ps, 2p < q < q+2 < p∗ s, p∗ s = Np N−ps is the fractional critical exponent, λ > 0 is a real parameter. By using the critical point theory for nonsmooth functionals and analytic techniques, the existence and multiplicity of positive solutions are obtained.

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