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1.
César Torres 《Mathematical Methods in the Applied Sciences》2017,40(13):4962-4973
In this paper, we are concerned with the existence of ground state solution for the following fractional differential equations with tempered fractional derivative: (FD) where α∈(1/2,1), λ>0, are the left and right tempered fractional derivatives, is the fractional Sobolev spaces, and . Assuming that f satisfies the Ambrosetti–Rabinowitz condition and another suitable conditions, by using mountain pass theorem and minimization argument over Nehari manifold, we show that (FD) has a ground state solution. Furthermore, we show that this solution is a radially symmetric solution. Copyright © 2017 John Wiley & Sons, Ltd. 相似文献
2.
We consider the Cauchy problem for the third‐order nonlinear Schrödinger equation where and is the Fourier transform. Our purpose in this paper is to prove the large time asymptoitic behavior of solutions for the defocusing case λ > 0 with a logarithmic correction under the non zero mass condition Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
3.
Ground state solutions for asymptotically periodic fractional Schrödinger–Poisson problems with asymptotically cubic or super‐cubic nonlinearities
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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
4.
Zhuan Ye 《Mathematical Methods in the Applied Sciences》2017,40(12):4595-4612
In this paper, we consider the 2D incompressible Boussinesq system with fractional Laplacian dissipation and thermal diffusion. On the basis of the previous works and some new observations, we show that the condition with suffices in order for the solution pair of velocity and temperature to remain smooth for all time. Copyright © 2017 John Wiley & Sons, Ltd. 相似文献
5.
The periodic solution bifurcated from homoclinic orbit for coupled ordinary differential equations
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We consider the problem of the periodic solutions bifurcated from a homoclinic orbit for a pair of coupled ordinary differential equations in . Assume that the autonomous system has a degenerate homoclinic solution γ in . A functional analytic approach is used to consider the existence of periodic solution for the autonomous system with periodic perturbations. By exponential dichotomies and the method of Lyapunov–Schmidt, the bifurcation function defined between two finite dimensional subspaces is obtained, where the zeros correspond to the existence of periodic solutions for the coupled ordinary differential equations near . Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
6.
Carlos Banquet Lucas C. F. Ferreira Élder J. Villamizar‐Roa 《Mathematical Methods in the Applied Sciences》2017,40(15):5613-5618
We consider a semilinear wave equation with nonlinear damping in the whole space . Local‐in‐time existence and uniqueness results are obtained in the class of Bessel‐potential spaces . Copyright © 2017 John Wiley & Sons, Ltd. 相似文献
7.
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
8.
Galerkin finite element method for generalized Forchheimer equation of slightly compressible fluids in porous media
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Thinh Kieu 《Mathematical Methods in the Applied Sciences》2017,40(12):4364-4384
We consider the generalized Forchheimer flows for slightly compressible fluids. Using Muskat's and Ward's general form of Forchheimer equations, we describe the fluid dynamics by a nonlinear degenerate parabolic equation for the density. We study Galerkin finite elements method for the initial boundary value problem. The existence and uniqueness of the approximation are proved. A prior estimates for the solutions in , time derivative in and gradient in , with a∈(0,1) are established. Error estimates for the density variable are derived in several norms for both continuous and discrete time procedures. Numerical experiments using backward Euler scheme confirm the theoretical analysis regarding convergence rates. Copyright © 2017 John Wiley & Sons, Ltd. 相似文献
9.
Infinitely many solutions for a class of fractional Hamiltonian systems via critical point theory
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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
10.
Global solutions to Keller‐Segel‐Navier‐Stokes equations with a class of large initial data in critical Besov spaces
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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
11.
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
12.
On the existence of positive least energy solutions for a coupled Schrödinger system with critical exponent
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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
13.
In this paper, we develop the energy argument in homogeneous Besov space framework to study the large time behavior of global‐in‐time strong solutions to the Cauchy problem of the three‐dimensional incompressible nematic liquid crystal flows with low regularity assumptions on initial data. More precisely, if the small initial data with 1 < p < ∞ and further assume that with 1 < q≤p and , then the global‐in‐time strong solution (u,d) to the nematic liquid crystal flows admits the following temporal decay rate: Here, is a constant unit vector. The highlight of our argument is to show that the ‐norms (with ) of solution are preserved along time evolution. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
14.
Pengtao Li Qixiang Yang Kai Zhao 《Mathematical Methods in the Applied Sciences》2017,40(18):6684-6701
In this paper, we apply wavelets to study the Triebel‐Lizorkin type oscillation spaces and identify them with the well‐known Triebel‐Lizorkin‐Morrey spaces. Further, we prove that Calderón‐Zygmund operators are bounded on . 相似文献
15.
In this paper, we prove the local‐in‐time existence and a blow‐up criterion of solutions in the Besov spaces for the Euler‐α equations of inviscid incompressible fluid flows in . We also establish the convergence rate of the solutions of the Euler‐α equations to the corresponding solutions of the Euler equations as the regularization parameter α approaches 0 in . Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
16.
Allal Ghanmi 《Mathematical Methods in the Applied Sciences》2017,40(18):7540-7545
We give 2 widest Mehler's formulas for the univariate complex Hermite polynomials , by performing double summations involving the products and . They can be seen as the complex analogues of the classical Mehler's formula for the real Hermite polynomials. The proof of the first one is based on a generating function giving rise to the reproducing kernel of the generalized Bargmann space of level m. The second Mehler's formula generalizes the one appearing as a particular case of the so‐called Kibble‐Slepian formula. The proofs we present here are direct and more simpler. Moreover, direct applications are given and remarkable identities are derived. 相似文献
17.
Global existence and optimal decay rates of solutions to conservation laws with diffusion‐type terms
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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
18.
Existence of positive solutions for integral boundary value problems of fractional differential equations on infinite interval
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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
19.
Global well‐posedness and blow‐up criterion for the periodic quasi‐geostrophic equations in Lei‐Lin‐Gevrey spaces
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Moez Benhamed 《Mathematical Methods in the Applied Sciences》2017,40(18):7488-7509
In this paper we consider a periodic 2‐dimensional quasi‐geostrophic equations with subcritical dissipation. We show the global existence and uniqueness of the solution for small initial data in the Lei‐Lin‐Gevrey spaces . Moreover, we establish an exponential type explosion in finite time of this solution. 相似文献
20.
Boundedness of solutions to parabolic–elliptic Keller–Segel systems with signal‐dependent sensitivity
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Kentarou Fujie Michael Winkler Tomomi Yokota 《Mathematical Methods in the Applied Sciences》2015,38(6):1212-1224
This paper deals with the parabolic–elliptic Keller–Segel system with signal‐dependent chemotactic sensitivity function, under homogeneous Neumann boundary conditions in a smooth bounded domain , with initial data satisfying u0 ≥ 0 and . The chemotactic sensitivity function χ(v) is assumed to satisfy The global existence of weak solutions in the special case is shown by Biler (Adv. Math. Sci. Appl. 1999; 9:347–359). Uniform boundedness and blow‐up of radial solutions are studied by Nagai and Senba (Adv. Math. Sci. Appl. 1998; 8:145–156). However, the global existence and uniform boundedness of classical nonradial solutions are left as an open problem. This paper gives an answer to the problem. Namely, it is shown that the system possesses a unique global classical solution that is uniformly bounded if , where γ > 0 is a constant depending on Ω and u0. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献