Existence and asymptotic behavior of the least energy solutions for fractional Choquard equations with potential well

Guo, Lun; Hu, Tingxi

doi:10.1002/mma.4653

Cited by 16 publications

(6 citation statements)

References 42 publications

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“…where p * s = Np N-sp . For more details about fractional Choquard equations, we refer the readers to [5,9,11,24,34,35]. Very recently, Mukherjee and Sreenadh [24] have obtained the following multiplicity result, extending the results in [10] in the local case, for the Brezis-Nirenberg type problem of semilinear fractional Choquard equation:…”

Section: Introduction and Main Resultsmentioning

confidence: 98%

Bifurcation results for the critical Choquard problem involving fractional p-Laplacian operator

Wang

Yang

2018

Bound Value Probl

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By using an abstract critical point theorem based on a pseudo-index related to the cohomological index, we prove the bifurcation results for the critical Choquard problems involving fractional p-Laplacian operator: (-) s p u = λ|u| p-2 u + |u| p * μ,s |x-y| μ dy |u| p * μ,s-2 u in , u = 0 in R N \ , where is a bounded domain in R N with Lipschitz boundary, λ is a real parameter, p ∈ (1, ∞), s ∈ (0, 1), N > sp, and p * μ,s = (N-μ 2)p N-sp is the critical exponent in the sense of Hardy-Littlewood-Sobolev inequality. These extend results in the literature for the fractional Choquard problems, and they are still new for a p-Laplacian case.

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Section: Introduction and Main Resultsmentioning

confidence: 98%

Bifurcation results for the critical Choquard problem involving fractional p-Laplacian operator

Wang

Yang

2018

Bound Value Probl

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“…For the critical Choquard equations in the sense of Hardy-Littlewood-Sobolev, Cassani and Zhang [12] developed a robust method to get the existence of ground states and qualitative properties of solutions, where they do not require the nonlinearity to enjoy monotonicity nor Ambrosetti-Rabinowitz-type conditions. For other existence results we refer to [6,8,23,24,31,48,52] and the references therein.…”

Section: Introduction and The Main Resultsmentioning

confidence: 99%

Multiplicity and concentration behaviour of solutions for a fractional Choquard equation with critical growth

Yang

Zhao

2020

Advances in Nonlinear Analysis

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In this paper, we study the singularly perturbed fractional Choquard equation $$\begin{equation*}\varepsilon^{2s}(-{\it\Delta})^su+V(x)u=\varepsilon^{\mu-3}(\int\limits_{\mathbb{R}^3}\frac{|u(y)|^{2^*_{\mu,s}}+F(u(y))}{|x-y|^\mu}dy)(|u|^{2^*_{\mu,s}-2}u+\frac{1}{2^*_{\mu,s}}f(u)) \, \text{in}\, \mathbb{R}^3, \end{equation*}$$ where ε > 0 is a small parameter, (−△)s denotes the fractional Laplacian of order s ∈ (0, 1), 0 < μ < 3, $2_{\mu ,s}^{\star }=\frac{6-\mu }{3-2s}$is the critical exponent in the sense of Hardy-Littlewood-Sobolev inequality and fractional Laplace operator. F is the primitive of f which is a continuous subcritical term. Under a local condition imposed on the potential V, we investigate the relation between the number of positive solutions and the topology of the set where the potential attains its minimum values. In the proofs we apply variational methods, penalization techniques and Ljusternik-Schnirelmann theory.

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“…For critical problem, Wang and Xiang [39] obtain the existence of infinitely many nontrivial solutions and the Brezis-Nirenberg type results can be founded in [33]. For other existence results we refer to [8,9,19,20,27,40,46] and the references therein.…”

Section: Introduction and The Main Resultsmentioning

confidence: 99%

Multiplicity and concentration of nontrivial nonnegative solutions for a fractional Choquard equation with critical exponent

Chen¹,

Li²,

Yang³

2019

RACSAM

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Existence and asymptotic behavior of the least energy solutions for fractional Choquard equations with potential well

Cited by 16 publications

References 42 publications

Bifurcation results for the critical Choquard problem involving fractional p-Laplacian operator

Bifurcation results for the critical Choquard problem involving fractional p-Laplacian operator

Multiplicity and concentration behaviour of solutions for a fractional Choquard equation with critical growth

Multiplicity and concentration of nontrivial nonnegative solutions for a fractional Choquard equation with critical exponent

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