共查询到20条相似文献,搜索用时 250 毫秒
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Zhouxin Li 《Journal of Differential Equations》2019,266(11):7264-7290
We prove the existence of positive solutions of the following singular quasilinear Schrödinger equations at critical growth via variational methods, where , , , , . It is interesting that we do not need to add a weight function to control . 相似文献
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We explicitly determine generators of cyclic codes over a non-Galois finite chain ring of length , where p is a prime number and k is a positive integer. We completely classify that there are three types of principal ideals of and four types of non-principal ideals of , which are associated with cyclic codes over of length . We then obtain a mass formula for cyclic codes over of length . 相似文献
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Rafael López 《Journal of Differential Equations》2019,266(7):3927-3941
We consider a smooth solution of the singular minimal surface equation defined in a bounded strictly convex domain of with constant boundary condition. If , we prove the existence a unique critical point of u. We also derive some and estimates of u by using the theory of maximum principles of Payne and Philippin for a certain family of Φ-functions. Finally we deduce an existence theorem of the Dirichlet problem when . 相似文献
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We prove the existence of solutions to the nonlinear Schrödinger equation in with a magnetic potential . Here V represents the electric potential, the index p is greater than 1. Along some sequence tending to zero we exhibit complex-value solutions that concentrate along some closed curves. 相似文献
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In this paper, we investigate the following modified nonlinear fourth-order elliptic equations where is the biharmonic operator, V is an indefinite potential, g grows subcritically and satisfies the Ambrosetti-Rabinowitz type condition with . Using Morse theory, we obtain nontrivial solutions of the above equations. Our result complements recent results in [17], where g has to be 3-superlinear at infinity. 相似文献
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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 studies the asymptotic behavior of smooth solutions to the generalized Hall-magneto-hydrodynamics system (1.1) with one single diffusion on the whole space . We establish that, in the inviscid resistive case, the energy vanishes and converges to a constant as time tends to infinity provided the velocity is bounded in ; in the viscous non-resistive case, the energy vanishes and converges to a constant provided the magnetic field is bounded in . In summary, one single diffusion, being as weak as or with small enough , is sufficient to prevent asymptotic energy oscillations for certain smooth solutions to the system. 相似文献
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Ryosuke Hyakuna 《Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire》2019,36(4):1081-1104
This paper is concerned with the Cauchy problem for the Hartree equation on with the nonlinearity of type . It is shown that a global solution with some twisted persistence property exists for data in the space under some suitable conditions on γ and spatial dimension . It is also shown that the global solution u has a smoothing effect in terms of spatial integrability in the sense that the map is well defined and continuous from to , which is well known for the solution to the corresponding linear Schrödinger equation. Local and global well-posedness results for hat -spaces are also presented. The local and global results are proved by combining arguments by Carles–Mouzaoui with a new functional framework introduced by Zhou. Furthermore, it is also shown that the global results can be improved via generalized dispersive estimates in the case of one space dimension. 相似文献
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We characterize all finite metabelian 2-groups G whose abelianizations are of type , with , and for which their commutator subgroups have . This is given in terms of the order of the abelianizations of the maximal subgroups and the structure of the abelianizations of those normal subgroups of index 4 in G. We then translate these group theoretic properties to give a characterization of number fields k with 2-class group , , such that the rank of where is the Hilbert 2-class field of k. In particular, we apply all this to real quadratic number fields whose discriminants are a sum of two squares. 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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In this paper, we investigate the existence of multiple radial sign-changing solutions with the nodal characterization for a class of Kirchhoff type problems where , are radial and bounded away from below by positive numbers. Under some weak assumptions on , by taking advantage of the Gersgorin disc's theorem and Miranda theorem, we develop some new analytic techniques and prove that this problem admits infinitely many nodal solutions having a prescribed number of nodes k, whose energy is strictly increasing in k. Moreover, the asymptotic behaviors of as are established. These results improve and generalize the previous results in the literature. 相似文献
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《Discrete Mathematics》2022,345(8):112902
For a simple graph G, denote by n, , and its order, maximum degree, and chromatic index, respectively. A graph G is edge-chromatic critical if and for every proper subgraph H of G. Let G be an n-vertex connected regular class 1 graph, and let be obtained from G by splitting one vertex of G into two vertices. Hilton and Zhao in 1997 conjectured that must be edge-chromatic critical if , and they verified this when . In this paper, we prove it for . 相似文献
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The existence of global attractors is proved for the MHD equations with damping terms and on a bounded domain . First we establish the well-posedness of strong solutions. Then, the continuity of the corresponding semigroup is verified under the assumption , which is guided by Gagliardo-Nirenberg inequality. Finally, the system is shown to possess an -global attractor and an -global attractor. 相似文献
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