Existence and concentration of ground state solutions for a class of nonlocal problem in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="d1e22" altimg="si11.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>

Qian, Xiaotao; Chao, Wen

doi:10.1016/j.na.2020.112170

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2024

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Cited by 6 publications

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“…However, we now face a new nonlocal term a − b Ð Ω j∇uj 2 dx, which is different from the well-known Kirchhoff type nonlocal term a + b Ð Ω j∇uj 2 dx. Now, there has been some results on the existence and multiplicity of nontrivial solutions to this new nonlocal problem (see [15][16][17][18][19][20][21][22]).…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

Multiple Nontrivial Solutions for a Nonlocal Problem with Sublinear Nonlinearity

Shi

Qian

2021

Advances in Mathematical Physics

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In this paper, we study the following nonlocal problem − a − b ∫ Ω ∇ u 2 d x Δ u = λ u + f x u p − 2 u , x ∈ Ω , u = 0 , x ∈ ∂ Ω , where a , b > 0 are constants, 1 < p < 2 , λ > 0 , f ∈ L ∞ Ω is a positive function, and Ω is a smooth bounded domain in ℝ N with N ≥ 3 . By variational methods, we obtain a pair of nontrivial solutions for the considered problem provided f ∞ is small enough.

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Section: Introduction and Main Resultsmentioning

confidence: 99%

Multiple Nontrivial Solutions for a Nonlocal Problem with Sublinear Nonlinearity

Shi

Qian

2021

Advances in Mathematical Physics

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Existence and concentration of ground state solutions for Kirchhoff type equations with general nonlinearities

Chen

2022

Math Methods in App Sciences

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In this paper, we study the following singularly perturbed Kirchhoff type equation in subcritical casewhereUnder some suitable conditions, we obtain that there exists a ground state solution of the equation concentrating at a global minimum of V in the semiclassical limit by applying some new techniques and subtle analyses. Moreover, we use Moser iteration to conquer the difficulty caused by the lack of Sobolev inequality.

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Multiple Positive Solutions for Kirchhoff-Type Problems Involving Supercritical and Critical Terms

Wu,

Suo,

Lei

2024

Qual. Theory Dyn. Syst.

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Existence and concentration of ground state solutions for a class of nonlocal problem in RN

Cited by 6 publications

References 16 publications

Multiple Nontrivial Solutions for a Nonlocal Problem with Sublinear Nonlinearity

Multiple Nontrivial Solutions for a Nonlocal Problem with Sublinear Nonlinearity

Existence and concentration of ground state solutions for Kirchhoff type equations with general nonlinearities

Multiple Positive Solutions for Kirchhoff-Type Problems Involving Supercritical and Critical Terms

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