Existence results for Kirchhoff equations with Hardy–Littlewood–Sobolev critical nonlinearity

Song, Yanli; Zhao, Fu Hai; Pu, Hongling; Shi, Shaoyun

doi:10.1016/j.na.2020.111900

Cited by 2 publications

(1 citation statement)

References 60 publications

(25 reference statements)

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“…al [21] studied the multiplicity results for such modified quasilinear Kirchhoff equations. Then for p = 2 and β = 0 in [37], the authors studied such problem. Also, for β = 0, we refer to the work in [20], which deals with the Choquard equations involving the modified quasilinear Schrödinger operator as in (1.1), without the Kirchhoff term.…”

Section: Introductionmentioning

confidence: 99%

Multiplicity results for $p$-Kirchhoff modified Schrödinger equations with Stein-Weiss type critical nonlinearity in $\mathbb R^N$

Biswas¹,

Goyal²,

Sreenadh³

2022

Preprint

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In this article, we consider the following modified quasilinear critical Kirchhoff-Schrödinger problem involving Stein-Weiss type nonlinearity:is the critical exponent with respect to the doubly weighted Hardy-Littlewood-Sobolev inequality (also called Stein-Weiss type inequality). Then by establishing a concentration-compactness argument for our problem, we show the existence of infinitely many nontrivial solutions to the equations with respect to the parameter λ by using Krasnoselskii's genus theory, symmetric mountain pass theorem and Z 2 -symmetric version of mountain pass theorem for different range of q. We further show that these solutions belong to L ∞ (R N ).

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Section: Introductionmentioning

confidence: 99%

Multiplicity results for $p$-Kirchhoff modified Schrödinger equations with Stein-Weiss type critical nonlinearity in $\mathbb R^N$

Biswas¹,

Goyal²,

Sreenadh³

2022

Preprint

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Multiple solutions for the quasilinear Choquard equation with Berestycki-Lions-type nonlinearities

Jia,

Yang

2024

Advances in Nonlinear Analysis

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In this article, we study the following quasilinear equation with nonlocal nonlinearity − Δ u − κ u Δ ( u 2 ) + λ u = ( ∣ x ∣ − μ * F ( u ) ) f ( u ) , in R N , -\Delta u-\kappa u\Delta \left({u}^{2})+\lambda u=\left({| x| }^{-\mu }* F\left(u))f\left(u),\hspace{1em}\hspace{0.1em}\text{in}\hspace{0.1em}\hspace{0.33em}{{\mathbb{R}}}^{N}, where κ \kappa is a parameter, N ≥ 3 N\ge 3 , μ ∈ ( 0 , N ) \mu \in \left(0,N) , F ( t ) = ∫ 0 t f ( s ) d s F\left(t)={\int }_{0}^{t}f\left(s){\rm{d}}s , and λ \lambda is a positive constant. We are going to analyze two cases: the L 2 {L}_{2} -norm of the solution is not confirmed and the L 2 {L}_{2} -norm of the solution is prescribed. Under the almost optimal assumptions on f f , we obtain the existence of a sequence of radial solutions for two cases.

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Existence results for Kirchhoff equations with Hardy–Littlewood–Sobolev critical nonlinearity

Cited by 2 publications

References 60 publications

Multiplicity results for $p$-Kirchhoff modified Schrödinger equations with Stein-Weiss type critical nonlinearity in $\mathbb R^N$

Multiplicity results for $p$-Kirchhoff modified Schrödinger equations with Stein-Weiss type critical nonlinearity in $\mathbb R^N$

Multiple solutions for the quasilinear Choquard equation with Berestycki-Lions-type nonlinearities

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