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Concentrating Solutions for a Fractional Kirchhoff Equation with Critical Growth [PDF]

Asymptotic Analysis, 2019
In this paper we consider the following class of fractional Kirchhoff equations with critical growth: [Formula: see text] where [Formula: see text] is a small parameter, [Formula: see text] are constants, [Formula: see text], [Formula: see text] is the fractional critical exponent, [Formula: see text] is the fractional Laplacian operator, V is a ...
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Existence and multiplicity of entire solutions for fractional p-Kirchhoff equations

Advances in Nonlinear Analysis, 2016
The purpose of this paper is mainly to investigate the existence of entire solutions of the stationary Kirchhoff type equations driven by the fractional p-Laplacian operator in ℝN.
Pucci Patrizia, Xiang Mingqi, Zhang Binlin   +2 more
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Final Value Problem for Parabolic Equation with Fractional Laplacian and Kirchhoff’s Term

Journal of Function Spaces, 2021
In this paper, we study a diffusion equation of the Kirchhoff type with a conformable fractional derivative. The global existence and uniqueness of mild solutions are established. Some regularity results for the mild solution are also derived.
Nguyen Hoang Luc, Devendra Kumar, Le Dinh Long, Ho Thi Kim Van   +3 more
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Existence of radial sign-changing solution for a fractional autonomous Kirchhoff equation

四川大学学报. 自然科学版, 2020
The existence of sign-changing solutions for a fractional autonomous Kirchhoff equation is considered in the whole space. We prove that this equation is equivalent to a fractional autonomous Schr&odinger system under appropriate conditions.
ZHANG Dan-dan, DING Ling
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Multiplicity Results of Solutions to Non-Local Magnetic Schrödinger–Kirchhoff Type Equations in ${\mathbb{R}}^N$

Axioms, 2022
In this paper, we establish the existence of a nontrivial weak solution to Schrödinger-kirchhoff type equations with the fractional magnetic field without Ambrosetti and Rabinowitz condition using mountain pass theorem under a suitable assumption of the ...
Kisoeb Park
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Superlinear Kirchhoff-type problems of the fractional p-Laplacian without the (AR) condition

Boundary Value Problems, 2018
In this paper, we study the following superlinear p-Kirchhoff-type equation: {M(∫R2N|u(x)−u(y)|p|x−y|N+psdxdy)(−△)psu(x)−λ|u|p−2u=g(x,u)in Ω,u=0in RN∖Ω, $$\begin{aligned} \textstyle\begin{cases} \mathcal{M} (\int_{\mathbb{R}^{2N}}\frac { \vert u(x)-u(y) \
Jiabin Zuo, Tianqing An, Mingwei Li
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Existence of Ground State Solutions for a Class of Non-Autonomous Fractional Kirchhoff Equations

Fractal and Fractional
We take a look at the fractional Kirchhoff problem in this paper. Using a variational approach, we show that there exists a ground state solution for this problem.
Guangze Gu, Changyang Mu, Zhipeng Yang
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Existence Results for Kirchhoff Nonlocal Fractional Equations

Kragujevac Journal of Mathematics
Fractional and nonlocal operators of elliptic type arise in a quite natural way in many different contexts. In this paper, we study the existence of solutions for a class of fractional equations, while the nonlinear part of the problem admits some perturbation property. We obtain some new criteria for existence of two and infinitely many solutions, using
Liao, Fang-Fang, Heidarkhani, Shapour, Salari, Amjad   +2 more
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Concentration of solutions for fractional Kirchhoff equations with discontinuous reaction

Zeitschrift für angewandte Mathematik und Physik, 2022
AbstractIn this paper, we consider the following fractional Kirchhoff equation with discontinuous nonlinearity$$\begin{aligned} \left\{ \begin{array}{ll} \left( \varepsilon ^{2\alpha }a+\varepsilon ^{4\alpha -3}b\int _{{\mathbb {R}}^3}|(-\Delta )^{\frac{\alpha }{2}} u|^2{{\mathrm{d}}}x\right) (-\Delta )^\alpha {u}+V(x)u = H(u-\beta )f(u) &{} \quad \
Zhisu Liu, Vicenţiu D. Rădulescu, Ziqing Yuan   +2 more
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Multiplicity and concentration of solutions for Kirchhoff equations with exponential growth

Bulletin of Mathematical Sciences
In this paper, we deal with fractional [Formula: see text]-Laplace Kirchhoff equations with exponential growth of the form 𝜀ps(a + b[u] s,pp)(−Δ) psu + Z(x)|u|p−2u = h(u)in ℝN, where [Formula: see text] is a positive parameter, [Formula: see text ...
Xueqi Sun, Yongqiang Fu, Sihua Liang
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