Existence and concentration of positive ground states for a 1-Laplacian problem in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="d1e35" altimg="si13.svg"><mml:msup><mml:mrow><mml:mi mathvariant="double-struck">R</mml:mi></mml:mrow><mml:mrow><mml:mi>N</mml:mi></mml:mrow></mml:msup></mml:math>

Che, Guofeng; He, Shi; Wang, Zewei

doi:10.1016/j.aml.2019.106045

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Introduction2

Guofeng Che Haibo Chen and Tsung-fang Wu1

(13)1

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2020

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Cited by 11 publications

(4 citation statements)

References 8 publications

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“…The 1-Laplace problem like (1) derived from image denoising and restoration is of crucial importance for many mathematical and physical fields introduced in [5]- [12]. Recently, more and more attention has been paid to p-Laplace operator ∆ p u = div(|∇u| p−2 ∇u), p ∈ [1, +∞).…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

Ground state solution for a non-autonomous 1-Laplacian problem involving periodic potential in ℝ N

Wang¹,

Chen²,

Li³

2022

Comptes Rendus. Mathématique

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Section: Introduction and Main Resultsmentioning

confidence: 99%

Ground state solution for a non-autonomous 1-Laplacian problem involving periodic potential in ℝ N

Wang¹,

Chen²,

Li³

2022

Comptes Rendus. Mathématique

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“…Similar to the arguments of [12,20,21], we give the definition of concentration of the solutions for problem (SP ε ). Definition 1.1.…”

Section: Guofeng Che Haibo Chen and Tsung-fang Wumentioning

confidence: 99%

Bound state positive solutions for a class of elliptic system with Hartree nonlinearity

Che¹,

Chen²,

Wu³

2020

Communications on Pure &Amp; Applied Analysis

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“…(1.6) possesses ground state solutions by using variational methods. For other work about the fractional Laplacian system, we would like to mention [13][14][15][16][17][18] and the references therein.…”

Section: (13)mentioning

confidence: 99%

Existence of positive ground state solutions to a nonlinear fractional Schrödinger system with linear couplings

Mao

Liu

2020

J Inequal Appl

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In this paper, we investigate a nonlinear fractional Schrödinger system with linear couplings as follows:where (-) α , α ∈ (0, 1), denotes the fractional Laplacian and λ > 0 is the coupling parameter. Under some assumptions, we prove the existence of positive ground state solutions to the above system with the help of the method of Nehari manifold and concentration compactness lemma. MSC: Primary 35J50; secondary 35A01; 35B40

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Existence and concentration of positive ground states for a 1-Laplacian problem in RN

Cited by 11 publications

References 8 publications

Ground state solution for a non-autonomous 1-Laplacian problem involving periodic potential in ℝ N

Ground state solution for a non-autonomous 1-Laplacian problem involving periodic potential in ℝ N

Bound state positive solutions for a class of elliptic system with Hartree nonlinearity

Existence of positive ground state solutions to a nonlinear fractional Schrödinger system with linear couplings

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