Fractional Kirchhoff-type equation with Hardy–Littlewood–Sobolev critical exponent

Su, Yu; Chen, Haibo

doi:10.1016/j.camwa.2019.03.052

Cited by 23 publications

(12 citation statements)

References 38 publications

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“…In [36], Pucci et al studied problem involving critical Choquard nonlinearity with fractional p-Laplacian. For related work on this type of problems, we refer to [22,27,28,39,41] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

Unbalanced (p,2)-fractional problems with critical growth

Kumar

Sreenadh

2021

Journal of Mathematical Analysis and Applications

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We study the existence, multiplicity and regularity results of non-negative solutions of following doubly nonlocal problem:where Ω ⊂ R n is a bounded domain with C 2 boundary ∂Ω, 0 < s 2 < s 1 < 1, n > 2s 1 , 1 < q < p < 2, 1 < r ≤ 2 * µ with 2 * µ = 2n−µ n−2s1 , λ, β > 0 and a ∈ L d d−q (Ω), for some q < d < 2 * s1 := 2n n−2s1 , is a sign changing function. We prove that each nonnegative weak solution of (P λ ) is bounded. Furthermore, we obtain some existence and multiplicity results using Nehari manifold method.

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Section: Introductionmentioning

confidence: 99%

Unbalanced (p,2)-fractional problems with critical growth

Kumar

Sreenadh

2021

Journal of Mathematical Analysis and Applications

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“…By considering the effects of change in the length of strings during vibration Kirchhoff in 18 extends the D'Alembert Wave equation. For recent works on existence and multiplicity results for Kirchhoff type equations we cite the works in 19–24 and references therein 25 . proved the existence and multiplicity of positive solution of the following critical growth Kirchhoff‐Choquard problem using Nehari manifold and Concentration‐compactness lemma for the case 1 < q < 2 and for

q = 2

using Mountain Pass lemma.…”

Section: Introductionmentioning

confidence: 99%

Multiple positive solutions for degenerate Kirchhoff equations with singular and Choquard nonlinearity

Rawat

Sreenadh

2021

Math Methods in App Sciences

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In this paper we study the existence, multiplicity, and regularity of positive weak solutions for the following Kirchhoff–Choquard problem: M()∬ℝ2Nfalse|ufalse(xfalse)−ufalse(yfalse)false|2false|x−yfalse|N+2s0.1emdxdyfalse(−normalΔfalse)su=λuγ+()∫normalΩfalse|ufalse(yfalse)false|2μ,s∗false|x−yfalse|μ0.1emdyfalse|ufalse|2μ,s∗−2u0.51emin0.51emnormalΩ,3emu=00.51emin0.51emℝN\normalΩ, where Ω is open bounded domain of ℝN with C2 boundary, N > 2s and s ∈ (0, 1). M models Kirchhoff‐type coefficient in particular, the degenerate case where Kirchhoff coefficient M is zero at zero. (− Δ)s is fractional Laplace operator, λ > 0 is a real parameter, γ ∈ (0, 1) and 2μ,s∗=2N−μN−2s is the critical exponent in the sense of Hardy–Littlewood–Sobolev inequality. We prove that each positive weak solution is bounded and satisfy Hölder regularity of order s. Furthermore, using the variational methods and truncation arguments, we prove the existence of two positive solutions.

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“…In fractional framework, for p = 2, by generalizing the idea of [29] in [13], the authors established the regularity result for doubly nonlocal equation involving subcritical growth in the sense of Hardy-Littlewood-Sobolev inequality. In [41], the authors studied the L ∞ (R) bound of the nonnegative ground state solution to some Choquard equation driven by fractional Laplacian with critical growth in the sense of Hardy-Littlewood-Sobolev inequality.…”

Section: Introductionmentioning

confidence: 99%

Regularity results for Choquard equations involving fractional $p$-Laplacian

Biswas¹,

Tiwari²

2020

Preprint

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In this article first we address the regularity of weak solution for a class of pfractional Choquard equations:where Ω ⊂ R N is a smooth bounded domain, 1 < p < ∞ and 0 < s < 1 such that sp < N, µ < min{N, 2sp} and f : Ω × R → R is a continuous function with at most critical growth condition (in the sense of Hardy-Littlewood-Sobolev inequality) and F is its primitive. Next for p ≥ 2 we discuss the Sobolev versus Hölder minimizers of the energy functional J associated to the above problem, and using that we establish the existence of the local minimizer of J in the fractional Sobolev space W s,p 0 (Ω).

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Fractional Kirchhoff-type equation with Hardy–Littlewood–Sobolev critical exponent

Cited by 23 publications

References 38 publications

Unbalanced (p,2)-fractional problems with critical growth

Unbalanced (p,2)-fractional problems with critical growth

Multiple positive solutions for degenerate Kirchhoff equations with singular and Choquard nonlinearity

Regularity results for Choquard equations involving fractional $p$-Laplacian

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