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1.
We study the non-linear minimization problem on with , and : where presents a global minimum α at with . In order to describe the concentration of around , one needs to calibrate the behavior of with respect to s. The model case is In a previous paper dedicated to the same problem with , we showed that minimizers exist only in the range , which corresponds to a dominant non-linear term. On the contrary, the linear influence for prevented their existence. The goal of this present paper is to show that for , and , minimizers do exist. 相似文献
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This paper deals with positive solutions of the fully parabolic system under mixed boundary conditions (no-flux and Dirichlet conditions) in a smooth bounded convex domain with positive parameters and nonnegative smooth initial data .Global existence and boundedness of solutions were shown if in Fujie–Senba (2017). In the present paper, it is shown that there exist blowup solutions satisfying . This result suggests that the system can be regard as a generalization of the Keller–Segel system, which has -dichotomy. The key ingredients are a Lyapunov functional and quantization properties of stationary solutions of the system in . 相似文献
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We are concerned with the following singularly perturbed Gross–Pitaevskii equation describing Bose–Einstein condensation of trapped dipolar quantum gases: where ε is a small positive parameter, , ? denotes the convolution, and is the angle between the dipole axis determined by and the vector x. Under certain assumptions on , we construct a family of positive solutions which concentrates around the local minima of V as . Our main results extend the results in J. Byeon and L. Jeanjean (2007) [6], which dealt with singularly perturbed Schrödinger equations with a local nonlinearity, to the nonlocal Gross–Pitaevskii type equation. 相似文献
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Teresa DAprile 《Journal of Differential Equations》2019,266(11):7379-7415
We are concerned with the existence of blowing-up solutions to the following boundary value problem where Ω is a smooth and bounded domain in such that , is a positive smooth function, N is a positive integer and is a small parameter. Here defines the Dirac measure with pole at 0. We find conditions on the function a and on the domain Ω under which there exists a solution blowing up at 0 and satisfying as . 相似文献
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In this paper, we study the existence and concentration behavior of minimizers for , here and where and are constants. By the Gagliardo–Nirenberg inequality, we get the sharp existence of global constraint minimizers of for when , and . For the case , we prove that the global constraint minimizers of behave like for some when c is large, where is, up to translations, the unique positive solution of in and , and . 相似文献
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We give some arithmetic-geometric interpretations of the moments , , and of the Sato–Tate group of an abelian variety A defined over a number field by relating them to the ranks of the endomorphism ring and Néron–Severi group of A. 相似文献
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Michael Winkler 《Journal of Functional Analysis》2019,276(5):1339-1401
The Keller–Segel–Navier–Stokes system
(?)
is considered in a bounded convex domain with smooth boundary, where and , and where and are given parameters.It is proved that under the assumption that be finite, for any sufficiently regular initial data satisfying and , the initial-value problem for (?) under no-flux boundary conditions for n and c and homogeneous Dirichlet boundary conditions for u possesses at least one globally defined solution in an appropriate generalized sense, and that this solution is uniformly bounded in with respect to the norm in .Moreover, under the explicit hypothesis that , these solutions are shown to stabilize toward a spatially homogeneous state in their first two components by satisfying Finally, under an additional condition on temporal decay of f it is shown that also the third solution component equilibrates in that in as . 相似文献