Anomalous pseudo-parabolic Kirchhoff-type dynamical model
Advances in Nonlinear Analysis, 2021 In this paper, we study an anomalous pseudo-parabolic Kirchhoff-type dynamical model aiming to reveal the control problem of the initial data on the dynamical behavior of the solution in dynamic control system. Firstly, the local existence of solution is
Dai Xiaoqiang +3 more
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The concentration-compactness principles for Ws,p(·,·)(ℝN) and application
Advances in Nonlinear Analysis, 2020 We obtain a critical imbedding and then, concentration-compactness principles for fractional Sobolev spaces with variable exponents. As an application of these results, we obtain the existence of many solutions for a class of critical nonlocal problems ...
Ho Ky, Kim Yun-Ho
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Well-posedness and blow-up results for a class of nonlinear fractional Rayleigh-Stokes problem
Advances in Nonlinear Analysis, 2022 In this article, we consider the fractional Rayleigh-Stokes problem with the nonlinearity term satisfies certain critical conditions. The local existence, uniqueness and continuous dependence upon the initial data of ε\varepsilon -regular mild solutions ...
Wang Jing Na +3 more
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Sign-Changing Solutions for the One-Dimensional Non-Local sinh-Poisson Equation
Advanced Nonlinear Studies, 2020 We study the existence of sign-changing solutions for a non-local version of the sinh-Poisson equation on a bounded one-dimensional interval I, under Dirichlet conditions in the exterior of I.
DelaTorre Azahara +2 more
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, 2020 The objective of this study is to present a new modification of the reduced differential transform method (MRDTM) to find an approximate analytical solution of a certain class of nonlinear fractional partial differential equations in particular ...
A. Khalouta, A. Kadem
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A complete study of the lack of compactness and existence results of a fractional Nirenberg equation via a flatness hypothesis, I [PDF]
, 2014 In this paper, we consider a nonlinear critical problem involving the fractional Laplacian operator arising in conformal geometry, namely the prescribed -curvature problem on the standard n- sphere n ≥ 2.
W. Abdelhedi, H. Chtioui, H. Hajaiej
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Least energy sign-changing solutions for a nonlocal anisotropic Kirchhoff type equation
Moroccan Journal of Pure and Applied Analysis, 2022 In this paper, we investigate the existence of sign-changing solutions for the following class of fractional Kirchhoff type equations with potential (1+b[u]α2)((-Δx)αu-Δyu)+V(x,y)u=f(x,y,u),(x,y)∈ℝN=ℝn×ℝm,\left( {1 + b\left[ u \right]_\alpha ^2} \right ...
Rahmani Mohammed +3 more
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Fractional Fokker-Planck-Kolmogorov type Equations and their Associated Stochastic Differential Equations [PDF]
, 2011 MSC 2010: 26A33, 35R11, 35R60, 35Q84, 60H10 Dedicated to 80-th anniversary of Professor Rudolf GorenfloThere is a well-known relationship between the Itô stochastic differential equations (SDEs) and the associated partial differential equations called ...
Hahn, Marjorie, Umarov, Sabir
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All functions are locally $s$-harmonic up to a small error [PDF]
, 2014 We show that we can approximate every function $f\in C^{k}(\bar{B_1})$ with a $s$-harmonic function in $B_1$ that vanishes outside a compact set. That is, $s$-harmonic functions are dense in $C^{k}_{\rm{loc}}$.
Dipierro, Serena +2 more
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Fractional Hardy-Sobolev equations with nonhomogeneous terms
Advances in Nonlinear Analysis, 2021 This paper deals with existence and multiplicity of positive solutions to the following class of nonlocal equations with critical nonlinearity:
Bhakta Mousomi +2 more
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