Results 11 to 20 of about 347 (175)

Existence of ground state for fractional Kirchhoff equation with L 2 $L^{2}$ critical exponents

Boundary Value Problems, 2020
In this paper, we consider a class of fractional Kirchhoff equations with L 2 $L^{2}$ critical exponents. By using the scaling technique and concentration-compactness principle we obtain the existence and nonexistence of ground state for fractional ...
Yaling Han, Yimin Zhang
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A class of p1(x, ⋅) & p2(x, ⋅)-fractional Kirchhoff-type problem with variable s(x, ⋅)-order and without the Ambrosetti-Rabinowitz condition in ℝN

Open Mathematics, 2022
In this article, we study a class of Kirchhoff-type equation driven by the variable s(x, ⋅)-order fractional p1(x, ⋅) & p2(x, ⋅)-Laplacian. With the help of three different critical point theories, we obtain the existence and multiplicity of solutions in
Bu Weichun, An Tianqing, Zuo Jiabin
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SOLUTIONS FOR THE KIRCHHOFF TYPE EQUATIONS WITH FRACTIONAL LAPLACIAN

Journal of Applied Analysis & Computation, 2020
Summary: Due to the singularity and nonlocality of the fractional Laplacian, the classical tools such as Sturm comparison, Wronskians, Picard-Lindelöf iteration, and shooting arguments (which are all purely local concepts) are not{ applicable} when analyzing solutions in the setting of the nonlocal operator \((-\Delta)^s\).
Jia, Yanping, Gao, Ying, Zhang, Guang
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Fractional weighted $ p $-Kirchhoff equations with general nonlinearity

Discrete and Continuous Dynamical Systems - S, 2023
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Xiang, Mingqi, Song, Chaoqun
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Multiple positive solutions for a fractional Kirchhoff type equation with logarithmic and singular nonlinearities

Electronic Journal of Qualitative Theory of Differential Equations, 2023
In this paper, we study the following fractional Kirchhoff type equation \begin{equation*} \begin{cases} \left(a+b\displaystyle\int_{\mathbb{R}^N}\int_{\mathbb{R}^N}\frac{|u(x)-u(y)|^p}{|x-y|^{N+ps}}dxdy\right)(-\Delta)_p^su=|u|^{q-2}u\ln |u|^2+\frac ...
Jun Lei
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Initial Boundary Value Problem for a Fractional Viscoelastic Equation of the Kirchhoff Type

Fractal and Fractional, 2022
In this paper, we study the initial boundary value problem for a fractional viscoelastic equation of the Kirchhoff type. In suitable functional spaces, we define a potential well.
Yang Liu, Li Zhang
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An Existence Result for Fractional Kirchhoff-Type Equations

Zeitschrift für Analysis und ihre Anwendungen, 2016
The aim of this paper is to study a class of nonlocal fractional Laplacian equations of Kirchhoff-type. More precisely, by using an appropriate analytical context on fractional Sobolev spaces, we establish the existence of one non-trivial weak solution for nonlocal fractional problems exploiting suitable variational methods.
Bisci, G., TULONE, Francesco
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Ground states to a Kirchhoff equation with fractional Laplacian

AIMS Mathematics, 2023
<abstract><p>The aim of this paper is to deal with the Kirchhoff type equation involving fractional Laplacian operator</p> <p><disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ \left(\alpha+\beta \int_{\mathbb{R}^{3}}|(-\Delta)^{\frac{s}{2}}\psi|^{2}\,\mathrm{d} x\right)(-\Delta)^{s}\psi+\kappa ...
Dengfeng Lu, Shuwei Dai
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The transient analysis for zero-input response of fractal RC circuit based on local fractional derivative

Alexandria Engineering Journal, 2020
Local fractional calculus has gained wide attention in the field of circuit design. In this paper, we propose the zero-input response(ZIR) of fractal RC circuit modeled by local fractional derivative(LFD) for the first time.
Kang-Jia Wang, Hong-Chang Sun, Zhe Fei
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Multiple solutions to the Kirchhoff fractional equation involving Hardy–Littlewood–Sobolev critical exponent

Boundary Value Problems, 2019
In this paper, we study a fractional Kirchhoff type equation with Hardy–Littlewood–Sobolev critical exponent. By using variational methods, we obtain the existence of mountain-pass type solution and negative energy solutions.
Jichao Wang, Jian Zhang, Yujun Cui
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