Advances in Nonlinear Analysis

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A fractional Kirchhoff problem involving a singular term and a critical nonlinearity
Advances in Nonlinear Analysis - Tập 8 Số 1 - Trang 645-660 - 2017
Alessio Fiscella
AbstractIn this paper, we consider the following critical nonlocal problem:\left\{\begin{aligned} &\displaystyle M\bigg{(}\iint_{\mathbb{R}^{2N}}\frac{% \lvert u(x)-u(y)\rvert^{2}}{\lvert x-y\rvert^{N+2s}}\,dx\,dy\biggr{)}(-\Delta)% ^{s}u=\frac{\lambda}{u^{\gamma}}+u^{2^{*}_{s}-1}&&\displaystyle\phantom{}\text% {in }\Omega,\\ \displaystyle u&\displaystyle>0&&\displaystyle\phantom{}\text{in }\Omega... hiện toàn bộ
Existence and multiplicity of entire solutions for fractional p-Kirchhoff equations
Advances in Nonlinear Analysis - Tập 5 Số 1 - Trang 27-55 - 2016
Patrizia Pucci, Mingqi Xiang, Binlin Zhang
Abstract 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 ℝ N . By using variational methods and topological degree theory, we prove multiplicity results depending on a real parameter λ and under suitable general integrability properties of the ratio between some powers o... hiện toàn bộ
Existence and general stabilization of the Timoshenko system of thermo-viscoelasticity of type III with frictional damping and delay terms
Advances in Nonlinear Analysis - Tập 7 Số 4 - Trang 547-569 - 2018
Miaomiao Chen, Wenjun Liu, Weican Zhou
Abstract In this paper, we consider the following Timoshenko system of thermo-viscoelasticity of type III with frictional damping and delay terms: { ρ 1 ⁢ φ t ⁢ t - K ⁢ ( φ x + ψ ) x = 0 , ( x , t ) ∈ ( 0 , 1 ) × ( 0 , ∞ ) , ρ 2 ⁢ ψ t ⁢ t - b ⁢ ψ x ⁢ x + K ⁢ ( φ x + ψ ) + β ⁢ θ x = 0 , ( x , t ) ∈ ( 0 , 1 ) × ( 0 , ∞ ) , ρ 3 ⁢ θ t ⁢ t - δ ⁢ θ x ⁢ x + γ ⁢ ψ t ⁢ t ⁢ x + ∫ 0 t g ⁢ ( t - s ) ⁢ θ x ⁢ x... hiện toàn bộ
The subelliptic ∞-Laplace system on Carnot–Carathéodory spaces
Advances in Nonlinear Analysis - Tập 2 Số 2 - Trang 213-233 - 2013
Nicholas Katzourakis
Abstract. Given a Carnot–Carathéodory space with associated frame of vector fields , we derive the subelliptic ∞-Laplace system for mappings , which reads in the limit of the subelliptic p-Laplacian as . Here is the horizontal gradient and is the projection on its nullspace. Next, we identify the variational principle characterizing the subelliptic ∞-Laplacian system, which is the “Euler–Lagrange ... hiện toàn bộ
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