共查询到20条相似文献,搜索用时 46 毫秒
1.
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
2.
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
3.
In this paper we study the following type of the Schrödinger–Poisson–Slater equation with critical growth where and . For the case of . We develop a novel perturbation approach, together with the well-known Mountion–Pass theorem, to prove the existence of positive ground states. For the case of , we obtain the nonexistence of nontrivial solutions by restricting the range of μ and also study the existence of positive solutions by the constrained minimization method. For the case of , we use a truncation technique developed by Brezis and Oswald [9] together with a measure representation concentration-compactness principle due to Lions [27] to prove the existence of radial symmetrical positive solutions for with some . The above results nontrivially extend some theorems on the subcritical case obtained by Ianni and Ruiz [18] to the critical case. 相似文献
4.
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
5.
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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7.
Qingbo Huang 《Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire》2019,36(7):1869-1902
We develop interior and regularity theories for -viscosity solutions to fully nonlinear elliptic equations , where T is approximately convex at infinity. Particularly, regularity theory holds if operator T is locally semiconvex near infinity and all eigenvalues of are at least as . regularity for some Isaacs equations is given. We also show that the set of fully nonlinear operators of regularity theory is dense in the space of fully nonlinear uniformly elliptic operators. 相似文献
8.
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
9.
We study ground states of two-component Bose–Einstein condensates (BEC) with trapping potentials in , where the intraspecies interaction and the interspecies interaction ?β are both attractive, , , and β are all positive. The existence and non-existence of ground states are classified completely by investigating equivalently the associated -critical constraint variational problem. The uniqueness and symmetry-breaking of ground states are also analyzed under different types of trapping potentials as , where () is fixed and w is the unique positive solution of in . The semi-trivial limit behavior of ground states is tackled in the companion paper [12]. 相似文献
10.
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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12.
In this paper, we study semilinear elliptic systems with critical nonlinearity of the form
(0.1)
for , Q has quadratic growth in ?u. Our work is motivated by elliptic systems for harmonic map and biharmonic map. When , such a system does not have smooth regularity in general for weak solutions, by a well-known example of J. Frehse. Classical results of harmonic map, proved by F. Hélein (for ) and F. Béthuel (for ), assert that a weak solution of harmonic map is always smooth. We extend Béthuel's result to general system (0.1), that a weak solution of the system is smooth for . For a fourth order semilinear elliptic system with critical nonlinearity which extends biharmonic map, we prove a similar result, that a weak solution of such system is always smooth, for . We also construct various examples, and these examples show that our regularity results are optimal in various sense. 相似文献
13.
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
14.
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
15.
In this paper, we consider the following nonlinear elliptic equation involving the fractional Laplacian with critical exponent: where and , is periodic in with . Under some natural conditions on K near a critical point, we prove the existence of multi-bump solutions where the centers of bumps can be placed in some lattices in , including infinite lattices. On the other hand, to obtain positive solution with infinite bumps such that the bumps locate in lattices in , the restriction on is in some sense optimal, since we can show that for , no such solutions exist. 相似文献
16.
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
17.
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
18.
We investigate a sharp Moser–Trudinger inequality which involves the anisotropic Dirichlet norm on for . Here F is convex and homogeneous of degree 1, and its polar represents a Finsler metric on . Under this anisotropic Dirichlet norm, we establish the Lions type concentration-compactness alternative. Then by using a blow-up procedure, we obtain the existence of extremal functions for this sharp geometric inequality. 相似文献
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With appropriate hypotheses on the nonlinearity f, we prove the existence of a ground state solution u for the problem where , V is a bounded continuous potential and F the primitive of f. We also show results about the regularity of any solution of this problem. 相似文献