共查询到20条相似文献,搜索用时 31 毫秒
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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
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Consider the Hénon equation with the homogeneous Neumann boundary condition where and . We are concerned on the asymptotic behavior of ground state solutions as the parameter . As , the non-autonomous term is getting singular near . The singular behavior of for large forces the solution to blow up. Depending subtly on the dimensional measure and the nonlinear growth rate p, there are many different types of limiting profiles. To catch the asymptotic profiles, we take different types of renormalization depending on p and . In particular, the critical exponent for the Sobolev trace embedding plays a crucial role in the renormalization process. This is quite contrasted with the case of Dirichlet problems, where there is only one type of limiting profile for any and a smooth domain Ω. 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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In this paper, we study an elliptic equation arising from the self-dual Maxwell gauged sigma model coupled with gravity. When the parameter τ equals 1 and there is only one singular source, we consider radially symmetric solutions. There appear three important constants: a positive parameter a representing a scaled gravitational constant, a nonnegative integer representing the total string number, and a nonnegative integer representing the total anti-string number. The values of the products play a crucial role in classifying radial solutions. By using the decay rates of solutions at infinity, we provide a complete classification of solutions for all possible values of and . This improves previously known results. 相似文献
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We consider a nonlinear Schrödinger system arising in a two-component Bose–Einstein condensate (BEC) with attractive intraspecies interactions and repulsive interspecies interactions in . We get ground states of this system by solving a constrained minimization problem. For some kinds of trapping potentials, we prove that the minimization problem has a minimizer if and only if the attractive interaction strength of each component of the BEC system is strictly less than a threshold . Furthermore, as , the asymptotical behavior for the minimizers of the minimization problem is discussed. Our results show that each component of the BEC system concentrates at a global minimum of the associated trapping potential. 相似文献
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Soyeun Jung 《Journal of Differential Equations》2012,253(6):1807-1861
By working with the periodic resolvent kernel and the Bloch-decomposition, we establish pointwise bounds for the Green function of the linearized equation associated with spatially periodic traveling waves of a system of reaction–diffusion equations. With our linearized estimates together with a nonlinear iteration scheme developed by Johnson–Zumbrun, we obtain -behavior () of a nonlinear solution to a perturbation equation of a reaction–diffusion equation with respect to initial data in recovering and slightly sharpening results obtained by Schneider using weighted energy and renormalization techniques. We obtain also pointwise nonlinear estimates with respect to two different initial perturbations , and , , respectively, sufficiently small and sufficiently large, showing that behavior is that of a heat kernel. These pointwise bounds have not been obtained elsewhere, and do not appear to be accessible by previous techniques. 相似文献
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《Nonlinear Analysis: Real World Applications》2007,8(4):1062-1078
This paper deals with the existence and nonexistence of nonconstant positive steady-state solutions to a ratio-dependent predator–prey model with diffusion and with the homogeneous Neumann boundary condition. We demonstrate that there exists satisfying for , such that if and , then the diffusion can create nonconstant positive steady-state solutions; whereas the diffusion cannot do provided . 相似文献
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Michael Winkler 《Journal of Differential Equations》2018,264(3):2310-2350
The chemotaxis system is considered under homogeneous Neumann boundary conditions in the ball , where and .Despite its great relevance as a model for the spontaneous emergence of spatial structures in populations of primitive bacteria, since its introduction by Keller and Segel in 1971 this system has been lacking a satisfactory theory even at the level of the basic questions from the context of well-posedness; global existence results in the literature are restricted to spatially one- or two-dimensional cases so far, or alternatively require certain smallness hypotheses on the initial data.For all suitably regular and radially symmetric initial data satisfying and , the present paper establishes the existence of a globally defined pair of radially symmetric functions which are continuous in and smooth in , and which solve the corresponding initial-boundary value problem for (?) with in an appropriate generalized sense. To the best of our knowledge, this in particular provides the first result on global existence for the three-dimensional version of (?) involving arbitrarily large initial data. 相似文献
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Tej-Eddine Ghoul Van Tien Nguyen Hatem Zaag 《Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire》2018,35(6):1577-1630
We consider the following parabolic system whose nonlinearity has no gradient structure: in the whole space , where and . We show the existence of initial data such that the corresponding solution to this system blows up in finite time simultaneously in u and v only at one blowup point a, according to the following asymptotic dynamics: with and . The construction relies on the reduction of the problem to a finite dimensional one and a topological argument based on the index theory to conclude. Two major difficulties arise in the proof: the linearized operator around the profile is not self-adjoint even in the case ; and the fact that the case breaks any symmetry in the problem. In the last section, through a geometrical interpretation of quantities of blowup parameters whose dimension is equal to the dimension of the finite dimensional problem, we are able to show the stability of these blowup behaviors with respect to perturbations in initial data. 相似文献
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In this paper we define odd dimensional unitary groups . These groups contain as special cases the odd dimensional general linear groups where R is any ring, the odd dimensional orthogonal and symplectic groups and where R is any commutative ring and further the first author's even dimensional unitary groups where is any form ring. We classify the E-normal subgroups of the groups (i.e. the subgroups which are normalized by the elementary subgroup ), under the condition that R is either a semilocal or quasifinite ring with involution and . Further we investigate the action of by conjugation on the set of all E-normal subgroups. 相似文献
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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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Elena Angelini Francesco Galuppi Massimiliano Mella Giorgio Ottaviani 《Journal of Pure and Applied Algebra》2018,222(4):950-965
We prove that a general polynomial vector in three homogeneous variables of degrees has a unique Waring decomposition of rank 7. This is the first new case we are aware of, and likely the last one, after five examples known since the 19th century and the binary case. We prove that there are no identifiable cases among pairs in three homogeneous variables of degree , unless , and we give a lower bound on the number of decompositions. The new example was discovered with Numerical Algebraic Geometry, while its proof needs Nonabelian Apolarity. 相似文献
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Stefan Steinerberger 《Journal of Functional Analysis》2018,274(6):1611-1630
Let be a bounded convex domain in the plane and consider If u assumes its maximum in , then the eccentricity of level sets close to the maximum is determined by the Hessian . We prove that is negative definite and give a quantitative bound on the spectral gap This is sharp up to constants. The proof is based on a new lower bound for Fourier coefficients whose proof has a topological component: if is continuous and has n sign changes, then This statement immediately implies estimates on higher derivatives of harmonic functions u in the unit ball: if u is very flat in the origin, then the boundary function has to have either large amplitude or many roots. It also implies that the solution of the heat equation starting with cannot decay faster than . 相似文献
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Fritz Gesztesy Lance L. Littlejohn Isaac Michael Richard Wellman 《Journal of Differential Equations》2018,264(4):2761-2801
In 1961, Birman proved a sequence of inequalities , for , valid for functions in . In particular, is the classical (integral) Hardy inequality and is the well-known Rellich inequality. In this paper, we give a proof of this sequence of inequalities valid on a certain Hilbert space of functions defined on . Moreover, implies ; as a consequence of this inclusion, we see that the classical Hardy inequality implies each of the inequalities in Birman's sequence. We also show that for any finite , these inequalities hold on the standard Sobolev space . Furthermore, in all cases, the Birman constants in these inequalities are sharp and the only function that gives equality in any of these inequalities is the trivial function in (resp., ). We also show that these Birman constants are related to the norm of a generalized continuous Cesàro averaging operator whose spectral properties we determine in detail. 相似文献