共查询到20条相似文献,搜索用时 46 毫秒
1.
Ground state solutions for asymptotically periodic fractional Schrödinger–Poisson problems with asymptotically cubic or super‐cubic nonlinearities
下载免费PDF全文
![点击此处可从《Mathematical Methods in the Applied Sciences》网站下载免费的PDF全文](/ch/ext_images/free.gif)
Sitong Chen Jiawu Peng Xianhua Tang 《Mathematical Methods in the Applied Sciences》2017,40(13):4948-4961
In this paper, we consider the following fractional Schrödinger–Poisson problem: where s,t∈(0,1],4s+2t>3,V(x),K(x), and f(x,u) are periodic or asymptotically periodic in x. We use the non‐Nehari manifold approach to establish the existence of the Nehari‐type ground state solutions in two cases: the periodic one and the asymptotically periodic case, by introducing weaker conditions uniformly in with and with constant θ0∈(0,1), instead of uniformly in and the usual Nehari‐type monotonic condition on f(x,τ)/|τ|3. Our results unify both asymptotically cubic or super‐cubic nonlinearities, which are new even for s=t=1. Copyright © 2017 John Wiley & Sons, Ltd. 相似文献
2.
In this paper, we study the existence of infinitely many homoclinic solutions for the second‐order self‐adjoint discrete Hamiltonian system , where , and are unnecessarily positive definites for all . By using the variant fountain theorem, we obtain an existence criterion to guarantee that the aforementioned system has infinitely many homoclinic solutions under the assumption that W(n,x) is asymptotically quadratic as | x | → + ∞ . Copyright © 2013 John Wiley & Sons, Ltd. 相似文献
3.
Infinitely many solutions for a class of fractional Hamiltonian systems via critical point theory
下载免费PDF全文
![点击此处可从《Mathematical Methods in the Applied Sciences》网站下载免费的PDF全文](/ch/ext_images/free.gif)
In this paper, we are concerned with the existence of infinitely many solutions for the following fractional Hamiltonian systems where , , and . The novelty of this paper is that, relaxing the conditions on the potential function W(t,x), we obtain infinitely many solutions via critical point theory. Our results generalize and improve some existing results in the literature. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
4.
In this paper, we study the nonexistence result for the weighted Lane–Emden equation: (0.1) and the weighted Lane–Emden equation with nonlinear Neumann boundary condition: (0.2) where f(|x|) and g(|x|) are the radial and continuously differential functions, is an upper half space in , and . Using the method of energy estimation and the Pohozaev identity of solution, we prove the nonexistence of the nontrivial solutions to problems 0.1 and 0.2 under appropriate assumptions on f(|x|) and g(|x|). Copyright © 2017 John Wiley & Sons, Ltd. 相似文献
5.
Global solutions to Keller‐Segel‐Navier‐Stokes equations with a class of large initial data in critical Besov spaces
下载免费PDF全文
![点击此处可从《Mathematical Methods in the Applied Sciences》网站下载免费的PDF全文](/ch/ext_images/free.gif)
Minghua Yang 《Mathematical Methods in the Applied Sciences》2017,40(18):7425-7437
In this article, we consider the Cauchy problem to Keller‐Segel equations coupled to the incompressible Navier‐Stokes equations. Using the Fourier frequency localization and the Bony paraproduct decomposition, let uF:=etΔu0; we prove that there exist 2 positive constants σ0 and C0 such that if the gravitational potential and the initial data (u0,n0,c0) satisfy for some p,q with and , then the global solutions can be established in critical Besov spaces. 相似文献
6.
It is well known that the time fractional equation where is the fractional time derivative in the sense of Caputo of u does not generate a dynamical system in the standard sense. In this paper, we study the algebraic properties of the solution operator T(t,s,τ) for that equation with u(s) = v. We apply this theory to linear time fractional PDEs with constant coefficients. These equations are solved by the Fourier multiplier techniques. It appears that their solution exhibits some singularity, which leads us to introduce a new kind of solution for abstract time fractional problems. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
7.
Two homoclinic solutions for a nonperiodic fourth‐order differential equation without coercive condition
下载免费PDF全文
![点击此处可从《Mathematical Methods in the Applied Sciences》网站下载免费的PDF全文](/ch/ext_images/free.gif)
In this paper, we investigate the existence of homoclinic solutions for a class of fourth‐order nonautonomous differential equations where w is a constant, and . By using variational methods and the mountain pass theorem, some new results on the existence of homoclinic solutions are obtained under some suitable assumptions. The interesting is that a(x) and f(x,u) are nonperiodic in x,a does not fulfil the coercive condition, and f does not satisfy the well‐known (AR)‐condition. Furthermore, the main result partly answers the open problem proposed by Zhang and Yuan in the paper titled with Homoclinic solutions for a nonperiodic fourth‐order differential equations without coercive conditions (see Appl. Math. Comput. 2015; 250:280–286). Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
8.
Ground state solutions and geometrically distinct solutions for generalized quasilinear Schrödinger equation
下载免费PDF全文
![点击此处可从《Mathematical Methods in the Applied Sciences》网站下载免费的PDF全文](/ch/ext_images/free.gif)
In this paper, we study the following generalized quasilinear Schrödinger equation where N≥3, is a C1 even function, g(0) = 1 and g′(s) > 0 for all s > 0. Under some suitable conditions, we prove that the equation has a ground state solution and infinitely many pairs ±u of geometrically distinct solutions. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
9.
In this paper, we study the following quasilinear Schrödinger equations: where Ω is a bounded smooth domain of , . Under some suitable conditions, we prove that this equation has three solutions of mountain pass type: one positive, one negative, and sign‐changing. Furthermore, if g is odd with respect to its second variable, this problem has infinitely many sign‐changing solutions. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
10.
Zhongyuan Liu 《Mathematical Methods in the Applied Sciences》2016,39(12):3461-3477
In this paper, we study the following biharmonic equation where , K(1) > 0,K′(1) > 0, B1(0) is the unit ball in (N≥6). We show that the aforementioned problem has infinitely many peak solutions, whose energy can be made arbitrarily large. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
11.
Global existence and optimal decay rates of solutions to conservation laws with diffusion‐type terms
下载免费PDF全文
![点击此处可从《Mathematical Methods in the Applied Sciences》网站下载免费的PDF全文](/ch/ext_images/free.gif)
Lijuan Wang 《Mathematical Methods in the Applied Sciences》2017,40(8):3040-3054
We consider the Cauchy problem on nonlinear scalar conservation laws with a diffusion‐type source term. Based on a low‐frequency and high‐frequency decomposition, Green's function method and the classical energy method, we not only obtain L2 time‐decay estimates but also establish the global existence of solutions to Cauchy problem when the initial data u0(x) satisfies the smallness condition on , but not on . Furthermore, by taking a time‐frequency decomposition, we obtain the optimal decay estimates of solutions. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
12.
In this paper, we study the following modified Kirchhoff‐type equations of the form: where a > 0, b ≥ 0, and . Under appropriate assumptions on V (x) and h(x,u), some existence results for positive solutions, negative solutions, and sequence of high energy solutions are obtained via a perturbation method. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
13.
Existence of ground state sign‐changing solutions for p‐Laplacian equations of Kirchhoff type
下载免费PDF全文
![点击此处可从《Mathematical Methods in the Applied Sciences》网站下载免费的PDF全文](/ch/ext_images/free.gif)
Jianhua Chen Xianhua Tang Zu Gao 《Mathematical Methods in the Applied Sciences》2017,40(14):5056-5067
In this paper, we prove the existence of ground state sign‐changing solutions for the following class of elliptic equation: where , and K(x) are positive continuous functions. Firstly, we obtain one ground state sign‐changing solution ub by using some new analytical skills and non‐Nehari manifold method. Furthermore, the energy of ub is strictly larger than twice that of the ground state solutions of Nehari type. We also establish the convergence property of ub as the parameter b↘0. Copyright © 2017 John Wiley & Sons, Ltd. 相似文献
14.
In this paper, by an approximating argument, we obtain infinitely many solutions for the following Hardy–Sobolev equation with critical growth: provided N > 6 + t, where and Ω is an open bounded domain in , which contains some points x0 = (0,z0). Copyright © 2013 John Wiley & Sons, Ltd. 相似文献
15.
On the existence of positive least energy solutions for a coupled Schrödinger system with critical exponent
下载免费PDF全文
![点击此处可从《Mathematical Methods in the Applied Sciences》网站下载免费的PDF全文](/ch/ext_images/free.gif)
Hongyu Ye 《Mathematical Methods in the Applied Sciences》2017,40(4):1032-1043
In this paper, we consider the following coupled Schrödinger system with critical exponent: where is a smooth bounded domain, λ > 0,μ≥0, and . Under certain conditions on λ and μ, we show that this problem has at least one positive least energy solution. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
16.
Global solutions of a two‐dimensional chemotaxis system with attraction and repulsion rotational flux terms
下载免费PDF全文
![点击此处可从《Mathematical Methods in the Applied Sciences》网站下载免费的PDF全文](/ch/ext_images/free.gif)
We consider the attraction–repulsion chemotaxis system with rotational flux terms where is a bounded domain with smooth boundary. Here, S1 and S2 are given parameter functions on [0,∞)2×Ω with values in . It is shown that for any choice of suitably regular initial data (u0,v0,w0) fulfilling a smallness condition on the norm of v0,w0 in L∞(Ω), the corresponding initial‐boundary value problem possesses a global bounded classical solution. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
17.
This paper is concerned with the following nonlinear fractional Schrödinger equation where ε>0 is a small parameter, V(x) is a positive function, 0<s<1, and . Under some suitable conditions, we prove that for any positive integer k, one can construct a nonradial sign‐changing (nodal) solutions with exactly k maximum points and k minimum points near the local minimum point of V(x). 相似文献
18.
This paper is concerned with the existence of positive solutions to a class of nonlocal boundary value problem of the p‐Kirchhoff type where is a bounded smooth domain and M,f, and g are continuous functions. The existence of a positive solution is stated through an iterative method based on mountain pass theorem. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
19.
This paper is concerned with the initial‐boundary value problem for one‐dimensional strongly damped wave equation involving p‐Laplacian. For p > 2 , we establish the existence of weak local attractors for this problem in . Under restriction 2 < p < 4, we prove that the semigroup, generated by the considered problem, possesses a strong global attractor in , and this attractor is a bounded subset of . Copyright © 2017 John Wiley & Sons, Ltd. 相似文献
20.
Existence of positive solutions for integral boundary value problems of fractional differential equations on infinite interval
下载免费PDF全文
![点击此处可从《Mathematical Methods in the Applied Sciences》网站下载免费的PDF全文](/ch/ext_images/free.gif)
Xiaochen Li Xiping Liu Mei Jia Yan Li Sha Zhang 《Mathematical Methods in the Applied Sciences》2017,40(6):1892-1904
In this paper, we consider a class of nonlinear fractional differential equations on the infinite interval with the integral boundary conditions By using Krasnoselskii fixed point theorem, the existence results of positive solutions for the boundary value problem in three cases and , are obtained, respectively. We also give out two corollaries as applications of the existence theorems and some examples to illustrate our results. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献