Multiplicity and concentration of nontrivial solutions for a class of fractional Kirchhoff equations with steep potential well

Shao, Liuyang; Chen, Haibo

doi:10.1002/mma.7932

Math Methods in App Sciences

2021

DOI: 10.1002/mma.7932

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Multiplicity and concentration of nontrivial solutions for a class of fractional Kirchhoff equations with steep potential well

Liuyang Shao

Haibo Chen

Abstract: 𝛼 2 u| 2 )dxwhere a, b, 𝜆 > 0 are parameters, 𝜇 > 0, and 0Under some simple assumptions on V, g, and f , we prove that problem (1.1) has at least two nontrivial solutions. Moreover, the phenomenon of concentration of solutions is obtained.

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Multiplicity and concentration of nontrivial solutions for Kirchhoff–Schrödinger–Poisson system with steep potential well

Shao,

Chen,

Wang

2024

Math Methods in App Sciences

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This article is about the following Kirchhoff–Schrödinger–Poisson system with steep potential well where are constants, , and . By using the variational principle, we overcome the difficulties caused by Poisson's term and obtain system (1.1) that has two nontrivial solutions under certain assumptions. Moreover, we study the concentration of solutions and obtain new conclusions of system (1.1). Finally, we present the case where the solution to system (1.1) does not exist.

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Multiplicity and concentration of nontrivial solutions for Kirchhoff–Schrödinger–Poisson system with steep potential well

Shao,

Chen,

Wang

2024

Math Methods in App Sciences

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The Existence, Uniqueness, and Multiplicity of Solutions for Two Fractional Nonlocal Equations

Wang

Wei

Zhou

2023

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This paper establishes the existence of unique and multiple solutions to two nonlocal equations with fractional operators. The main results are obtained using the variational method and algebraic analysis. The conclusion is that there exists a constant λ*>0 such that the equations have only three, two, and one solution, respectively, for λ∈(0,λ*), λ=λ*, and λ>λ*. The main conclusions fill the gap in the knowledge of this kind of fractional-order problem.

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Multiplicity and concentration of nontrivial solutions for a class of fractional Kirchhoff equations with steep potential well

Abstract: 𝛼 2 u| 2 )dxwhere a, b, 𝜆 > 0 are parameters, 𝜇 > 0, and 0Under some simple assumptions on V, g, and f , we prove that problem (1.1) has at least two nontrivial solutions. Moreover, the phenomenon of concentration of solutions is obtained.

Cited by 2 publications

References 26 publications

Multiplicity and concentration of nontrivial solutions for Kirchhoff–Schrödinger–Poisson system with steep potential well

Multiplicity and concentration of nontrivial solutions for Kirchhoff–Schrödinger–Poisson system with steep potential well

The Existence, Uniqueness, and Multiplicity of Solutions for Two Fractional Nonlocal Equations

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