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We consider the fractional Hartree equation in the -supercritical case, and find a sharp threshold of the scattering versus blow-up dichotomy for radial data: If and , then the solution is globally well-posed and scatters; if and , the solution blows up in finite time. This condition is sharp in the sense that the solitary wave solution is global but not scattering, which satisfies the equality in the above conditions. Here, Q is the ground-state solution for the fractional Hartree equation. 相似文献
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Liangchen Wang Chunlai Mu Xuegang Hu Pan Zheng 《Journal of Differential Equations》2018,264(5):3369-3401
This paper deals with a two-competing-species chemotaxis system with consumption of chemoattractantunder homogeneous Neumann boundary conditions in a bounded domain () with smooth boundary, where the initial data and are non-negative and the parameters , , and . The chemotactic function () is smooth and satisfying some conditions. It is proved that the corresponding initial–boundary value problem possesses a unique global bounded classical solution if one of the following cases hold: for ,(i) and(ii) .Moreover, we prove asymptotic stabilization of solutions in the sense that:? If and , then any global bounded solution exponentially converge to as ;? If and , then any global bounded solution exponentially converge to as ;? If and , then any global bounded solution algebraically converge to as . 相似文献
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For fractional Navier–Stokes equations and critical initial spaces X, one used to establish the well-posedness in the solution space which is contained in . In this paper, for heat flow, we apply parameter Meyer wavelets to introduce Y spaces where is not contained in . Consequently, for , we establish the global well-posedness of fractional Navier–Stokes equations with small initial data in all the critical oscillation spaces. The critical oscillation spaces may be any Besov–Morrey spaces or any Triebel–Lizorkin–Morrey spaces where . These critical spaces include many known spaces. For example, Besov spaces, Sobolev spaces, Bloch spaces, Q-spaces, Morrey spaces and Triebel–Lizorkin spaces etc. 相似文献
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Huyuan Chen Patricio Felmer Jianfu Yang 《Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire》2018,35(3):729-750
In this paper, we study the elliptic problem with Dirac mass
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where , , , is the Dirac mass at the origin and the potential V is locally Lipchitz continuous in , with non-empty support and satisfying with , and . We obtain two positive solutions of (1) with additional conditions for parameters on , p and k. The first solution is a minimal positive solution and the second solution is constructed via Mountain Pass Theorem. 相似文献
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In this work, we prove the existence of convex solutions to the following k-Hessian equation in the neighborhood of a point , where , is nonnegative near , and . 相似文献