共查询到20条相似文献,搜索用时 46 毫秒
1.
Ilyas Hashimoglu
mer Akn Khanlar R. Mamedov 《Mathematical Methods in the Applied Sciences》2019,42(7):2231-2243
In this article, we investigate the discreteness and some other properties of the spectrum for the Schrödinger operator L defined by the formula on the space L2(H, [0, ∞)) , where H is a Hilbert space. For the first time, an estimate is obtained for sum of the s‐numbers of the inverse Schrödinger operator. The obtained results were applied to the Laplace's equation in an angular region. 相似文献
2.
Qihong Shi Xiao‐Bing Zhang Changyou Wang Shu Wang 《Mathematical Methods in the Applied Sciences》2019,42(11):3929-3941
We investigate the blowup solutions to the Klein‐Gordon‐Schrödinger (KGS) system with power nonlinearity in spatial dimensions (N ≥ 2). Relying on a Lyapunov functional, we establish a perturbed virial‐type identity and prove the existence of blowup solutions for the system with a negative energy and small mass. Moreover, we obtain a new finite‐time blowup result of solutions to KGS system in the energy space by constructing a differential inequality. 相似文献
3.
Congming Peng Ying Zhang Caochuan Ma 《Mathematical Methods in the Applied Sciences》2019,42(18):6896-6905
The purpose of this work is to investigate the blow‐up dynamics of L2?critical focusing inhomogeneous fractional nonlinear Schrödinger equation: with 0<b<1. For this, we establish a new compactness lemma related to the equation. By applying this lemma, we study the dynamical behavior for blow‐up solutions for initial data satisfying , where Q is the ground state solution of our problem. 相似文献
4.
Hua Huang Shanlin Huang Quan Zheng Zhiwen Duan 《Mathematical Methods in the Applied Sciences》2019,42(9):3315-3326
We consider the inverse backscattering problem for the Schrödinger operator H = ?Δ + V on , n ≥ 3, as well as the higher‐order Schrödinger operator ( ? Δ)m + V, m = 2,3,…. We show that in some suitable Banach spaces, the map from the potential to the backscattering amplitude is a local diffeomorphism. This kind of problem (for m = 1) was studied by Eskin and Ralston [Comm. Math. Phys., 124(2), 169‐215 (1989)], where they assumed that . In this paper, we replace the assumption on V with certain decay assumption at infinity. 相似文献
5.
Mohammad Ramezani 《Mathematical Methods in the Applied Sciences》2019,42(14):4640-4663
In this work, we present numerical analysis for nonlinear multi‐term time fractional differential equation which involve Caputo‐type fractional derivatives for . The proposed method is based on utilization of fractional B‐spline basics in collocation method. The scheme can be readily obtained efficient and quite accurate with less computational work numerical result. The proposal approach transform nonlinear multi‐term time fractional differential equation into a suitable linear system of algebraic equations which can be solved by a suitable numerical method. The numerical experiments will be verify to demonstrate the effectiveness of our method for solving one‐ and two‐dimensional multi‐term time fractional differential equation. 相似文献
6.
In this paper, the existence and multiplicity of positive solutions is established for Schrödinger‐Poisson system of the form where 0 ∈ Ω is a smooth bounded domain in , , and λ > 0 is a real parameter. Combining with the variational method and Nehari manifold method, two positive solutions of the system are obtained. 相似文献
7.
Víctor Barrera‐Figueroa Vladimir S. Rabinovich 《Mathematical Methods in the Applied Sciences》2019,42(15):5072-5093
In this paper, we consider one‐dimensional Schrödinger operators Sq on with a bounded potential q supported on the segment and a singular potential supported at the ends h0, h1. We consider an extension of the operator Sq in defined by the Schrödinger operator and matrix point conditions at the ends h0, h1. By using the spectral parameter power series method, we derive the characteristic equation for calculating the discrete spectra of operator . Moreover, we provide closed‐form expressions for the eigenfunctions and associate functions in the Jordan chain given in the form of power series of the spectral parameter. The validity of our approach is proven in several numerical examples including self‐adjoint and nonself‐adjoint problems involving general point interactions described in terms of δ‐ and δ′‐distributions. 相似文献
8.
Quanqing Li Kaimin Teng Xian Wu Wenbo Wang 《Mathematical Methods in the Applied Sciences》2019,42(5):1480-1487
In this paper, we study the following fractional Schrödinger equation with critical or supercritical growth where 0 < s < 1, N > 2s, λ > 0, , , ( ? Δ)s denotes the fractional Laplacian of order s and f is a continuous superlinear but subcritical function. Under some suitable conditions, we prove that the equation has a nontrivial solution for small λ > 0 by variational methods. Our main contribution is related to the fact that we are able to deal with the case . 相似文献
9.
10.
Raúl Castillo Prez Vladislav V. Kravchenko Sergii M. Torba 《Mathematical Methods in the Applied Sciences》2019,42(15):5106-5117
A method for the computation of scattering data and of the Green function for the one‐dimensional Schrödinger operator with a decaying potential is presented. It is based on representations for the Jost solutions in the case of a compactly supported potential obtained in terms of Neumann series of Bessel functions (NSBF). The representations are used for calculating a complete orthonormal system of generalized eigenfunctions of the operator H, which in turn allow one to compute the scattering amplitudes and the Green function of the operator H?λ with . 相似文献
11.
The coupled Klein–Gordon–Schrödinger equation is reduced to a nonlinear ordinary differential equation (ODE) by using Lie classical symmetries, and various solutions of the nonlinear ODE are obtained by the modified ‐expansion method proposed recently. With the aid of solutions of the nonlinear ODE, more explicit traveling wave solutions of the coupled Klein–Gordon–Schrödinger equation are found out. The traveling wave solutions are expressed by the hyperbolic functions, trigonometric functions, and rational functions. Copyright © 2012 John Wiley & Sons, Ltd. 相似文献
12.
In this paper, we consider the following Schrödinger‐Poisson system: where parameters α,β∈(0,3),λ>0, , , and are the Hardy‐Littlewood‐Sobolev critical exponents. For α<β and λ>0, we prove the existence of nonnegative groundstate solution to above system. Moreover, applying Moser iteration scheme and Kelvin transformation, we show the behavior of nonnegative groundstate solution at infinity. For β<α and λ>0 small, we apply a perturbation method to study the existence of nonnegative solution. For β<α and λ is a particular value, we show the existence of infinitely many solutions to above system. 相似文献
13.
Ground state of solutions for a class of fractional Schrödinger equations with critical Sobolev exponent and steep potential well 下载免费PDF全文
In this paper, we study the following fractional Schrödinger equations: (1) where (?△)α is the fractional Laplacian operator with , 0≤s ≤2α , λ >0, κ and β are real parameter. is the critical Sobolev exponent. We prove a fractional Sobolev‐Hardy inequality and use it together with concentration compact theory to get a ground state solution. Moreover, concentration behaviors of nontrivial solutions are obtained when the coefficient of the potential function tends to infinity. 相似文献
14.
This paper is concerned with the initial value problem for the fourth‐order nonlinear Schrödinger type equation related to the theory of vortex filament. By deriving a fundamental estimate on dyadic blocks for the fourth‐order Schrödinger through the [k,Z]‐multiplier norm method. we establish multilinear estimates for this nonlinear fourth‐order Schrödinger type equation. The local well‐posedness for initial data in with s > 1 ∕ 2 is implied by the multilinear estimates. Copyright © 2012 John Wiley & Sons, Ltd. 相似文献
15.
《Mathematical Methods in the Applied Sciences》2018,41(2):615-645
In this paper, we deal with the multiplicity and concentration of positive solutions for the following fractional Schrödinger‐Kirchhoff type equation where ε>0 is a small parameter, is the fractional Laplacian, M is a Kirchhoff function, V is a continuous positive potential, and f is a superlinear continuous function with subcritical growth. By using penalization techniques and Ljusternik‐Schnirelmann theory, we investigate the relation between the number of positive solutions with the topology of the set where the potential attains its minimum. 相似文献
16.
V.S. Rabinovich R. Castillo‐Pérez F. Urbano‐Altamirano 《Mathematical Methods in the Applied Sciences》2013,36(7):761-772
The main aim of the paper is the study of essential spectra of electromagnetic Schrödinger operators with variable potentials in cylindric domains , where is a bounded domain with a smooth boundary provided by admissible boundary conditions. Applying the limit operators method, we obtain explicit estimates of the essential spectrum for a wide class of quantum waveguides. We also consider a numerical example of calculations of the discrete spectrum of horizontally stratified quantum waveguides applying a method of the decomposition of solutions of spectral problems for one‐dimensional Schrödinger operators as a power series with respect to the spectral parameter. Copyright © 2012 John Wiley & Sons, Ltd. 相似文献
17.
Guixiang Xu 《Mathematical Methods in the Applied Sciences》2014,37(17):2746-2771
In this paper, we show the scattering and blow up result of the solution for some coupled nonlinear Schrödinger system with static energy less than that of the ground state in , where . We first use the Nehari manifold approach and the Schwarz symmetrization technique to construct the ground state and obtain the threshold energy of scattering solution, then use Payne–Sattinger's potential well argument and Kenig–Merle's compactness‐rigidity argument to show the aforementioned dichotomy result. As we know, it is the first attempt to show the scattering result for the coupled nonlinear Schrödinger system. Copyright © 2013 John Wiley & Sons, Ltd. 相似文献
18.
Finite‐dimensional global attractor for a semi‐discrete fractional nonlinear Schrödinger equation 下载免费PDF全文
Caterina Calgaro Olivier Goubet Ezzeddine Zahrouni 《Mathematical Methods in the Applied Sciences》2017,40(15):5563-5574
We consider a semi‐discrete in time Crank–Nicolson scheme to discretize a weakly damped forced nonlinear fractional Schrödinger equation u t ?i (?Δ)α u +i |u |2u +γ u =f for considered in the the whole space . We prove that such semi‐discrete equation provides a discrete infinite‐dimensional dynamical system in that possesses a global attractor in . We show also that if the external force is in a suitable weighted Lebesgue space, then this global attractor has a finite fractal dimension. Copyright © 2017 John Wiley & Sons, Ltd. 相似文献
19.
Local well‐posedness of critical nonlinear Schrödinger equation on Zoll manifolds of odd‐growth 下载免费PDF全文
Tengfei Zhao 《Mathematical Methods in the Applied Sciences》2016,39(12):3226-3242
In this paper, we study the nonlinear Schrödinger equation on Zoll manifolds with odd order nonlinearities. We will obtain the local well‐poesdness in the critical space . This extends the recent results in the literature to the Zoll manifolds of dimension d≥2 with general odd order nonlinearities and also partially improves the previous results in the subcritical spaces of Yang to the critical cases. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
20.
Jos Vanterler da C. Sousa Fabio G. Rodrigues Edmundo Capelas de Oliveira 《Mathematical Methods in the Applied Sciences》2019,42(9):3033-3043
In this paper, using the Riemann‐Liouville fractional integral with respect to another function and the ψ?Hilfer fractional derivative, we propose a fractional Volterra integral equation and the fractional Volterra integro‐differential equation. In this sense, for this new fractional Volterra integro‐differential equation, we study the Ulam‐Hyers stability and, also, the fractional Volterra integral equation in the Banach space, by means of the Banach fixed‐point theorem. As an application, we present the Ulam‐Hyers stability using the α‐resolvent operator in the Sobolev space . 相似文献