期刊：
TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS,2017年49(1):165-182 ISSN：1230-3429
通讯作者：
Liu, Zhisu
作者机构：
[Liu, Zhisu] Univ South China, Sch Math & Phys, Hengyang 421001, Hunan, Peoples R China.;[Luo, Chaoliang] Hunan Univ Technol, Coll Sci & Technol, Zhuzhou 412008, Hunan, Peoples R China.
通讯机构：
[Liu, Zhisu] U;Univ South China, Sch Math & Phys, Hengyang 421001, Hunan, Peoples R China.
关键词：
We study the existence of positive ground state solutions for the nonlinear Kirchhoff type equation $$ \begin{cases} \displaystyle -\bigg(a+b\int_{\mathbb R^3}|\nabla u|^2\bigg)\Delta {u}+V(x)u =f(u) & \mbox{in }\mathbb R^3;\\ u\in H^1(\mathbb R^3);\quad u> 0 & \mbox{in } \mathbb R^3;\end{cases} $$ where $a;b> 0$ are constants;$f\in C(\mathbb R;\mathbb R)$ has general critical growth. We generalize a Berestycki-Lions theorem about the critical case of Schrödinger equation to Kirchhoff type equation via variational methods. Moreover;some subcritical works on Kirchhoff type equation are extended to the current critical case. Published: 2017 First available in Project Euclid: 11 April 2017 zbMATH: 1375.35188 MathSciNet: MR3635641 Digital Object Identifier: 10.12775/TMNA.2016.068
摘要：
We study the existence of positive ground state solutions for the nonlinear Kirchhoff type equation $$ \begin{cases} \displaystyle -\bigg(a+b\int_{\mathbb R^3}|\nabla u|^2\bigg)\Delta {u}+V(x)u =f(u) & \mbox{in }\mathbb R^3, \\ u\in H^1(\mathbb R^3), \quad u> 0 & \mbox{in } \mathbb R^3, \end{cases} $$ where $a,b> 0$ are constants, $f\in C(\mathbb R,\mathbb R)$ has general critical growth. We generalize a Berestycki-Lions theorem about the critical case of Schrödinger equation to Kirchhoff type equation via variational methods. Moreover, some subcritical works on Kirchhoff type equation are extended to the current critical case.
作者机构：
[Yang, Liu] Hengyang Normal Univ, Dept Math & Comp Sci, Hengyang 421008, Hunan, Peoples R China.;[Ouyang, Zigen; Liu, Zhisu] Univ South China, Sch Math & Phys, Hengyang 421001, Hunan, Peoples R China.
通讯机构：
[Liu, Zhisu] U;Univ South China, Sch Math & Phys, Hengyang 421001, Hunan, Peoples R China.
关键词：
Multiplicity;Kirchhoff type equation;Critical growth
摘要：
In this paper, we study the following Kirchhoff type equation with critical growth {-(a + b integral(Omega) vertical bar del u vertical bar(2)dx) del u = lambda u + mu vertical bar u vertical bar(2)u + vertical bar u vertical bar(4)u in Omega, u = 0 on partial derivative Omega, where a > 0, b >= 0 and Omega is a smooth bounded domain in R-3. When the real parameter mu is larger than some positive constant, we investigate the multiplicity of nontrivial solutions for the above problem with parameter lambda belonging to a left neighborhood of the Dirichlet eigenvalue of the Laplacian operator -Delta. (C) 2016 Elsevier Ltd. All rights reserved.
摘要：
In this paper, we study the multiplicity and concentration of solutions for the following critical fractional Schrödinger–Poisson system: \begin{eqnarray*} \left\{ \begin{array}{ll} \epsilon^{2s}(-\triangle)^{s} {u}+ V(x)u+\phi u =f(u)+|u|^{2^*_{s}-2}u &\mbox{in}\,\,\R^3, \\[2.5mm] \epsilon^{2t}(-\triangle)^{t}{\phi}=u^2 &\mbox{in}\,\, \R^3, \end{array} \right. \end{eqnarray*} where <i>ϵ<i/>> 0 is a small parameter, (− △ )<sup><i>α<i/><sup/> denotes the fractional Laplacian of order <i>α<i/> = <i>s,t<i/> ∈ (0,1), where 2<sub><i>α<i/><sub/><sup>∗<sup/>6/3−2α is the fractional critical exponent in Dimension 3; <i>V<i/> ∈ <i>C<i/><sup>1<sup/>(ℝ<sup>3<sup/>,ℝ<sup>+<sup/>) and <i>f<i/> is subcritical. We first prove that for <i>ϵ<i/>> 0 sufficiently small, the system has a positive ground state solution. With minimax theorems and Ljusternik–Schnirelmann theory, we investigate the relation between the number of positive solutions and the topology of the set where <i>V<i/> attains its minimum for small <i>ϵ<i/>. Moreover, each positive solution <i>u<i/><sub><i>ϵ<i/><sub/> converges to the least energy solution of the associated limit problem and concentrates around a global minimum point of <i>V<i/>.
作者机构：
[Liu, Zhisu] Univ South China, Sch Math & Phys, Hengyang 421001, Hunan, Peoples R China.;[Guo, Shangjiang; Fang, Yanqin] Hunan Univ, Coll Math & Econometr, Changsha 410082, Hunan, Peoples R China.
通讯机构：
[Guo, Shangjiang] H;Hunan Univ, Coll Math & Econometr, Changsha 410082, Hunan, Peoples R China.
关键词：
Kirchhoff type elliptic problem;critical growth;variational method;local compactness lemma;35J05;35J65;35Q51
摘要：
In this paper, we study the following Kirchhoff type elliptic problem with critical growth: {-(a + b integral(R4) vertical bar del u vertical bar(2) dx) Delta u + u = f(u) + beta vertical bar u vertical bar(2)u in R-4, u is an element of H-1(R-4), u > 0 in R-4, where a, beta > 0, and b >= 0, and the nonlinear growth term vertical bar u vertical bar(2)u reaches the Sobolev critical exponent since 2* = 4 for four spatial dimensions. In a non-radial symmetric function space, we establish a local compactness splitting lemma of critical version to investigate the existence of positive ground state solutions. (C) 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
摘要：
Graphene nanoribbons (GNRs) recently have drawn much interest because of their novel electronic properties such as well-controlled electronic structures, high Seebeck coefficient, and intriguing electronic transport. For the thermoelectric energy conversion, GNRs are thought to be rather poor candidates because of too high phonon thermal conductance, though they own good electronic conduction. Thus, the reduction of the phonon thermal conductance of GNRs is particularly important for their thermoelectric applications. Several methods such as strain, structural defects, etc., have been proposed to reduce the phonon thermal conductance of GNRs. In these methods, however, a central difficulty is that reducing the phonon thermal conductance always brings the adverse effects to the electron transport, which limits the further improvement of the thermoelectric efficiency of GNRs.
作者机构：
[Zhang, Chunhong] Hunan Vocat Coll Sci & Technol, Dept Publ Courses, Changsha 410004, Hunan, Peoples R China.;[Liu, Zhisu] Univ South China, Sch Math & Phys, Hengyang 421001, Hunan, Peoples R China.
通讯机构：
[Liu, Zhisu] U;Univ South China, Sch Math & Phys, Hengyang 421001, Hunan, Peoples R China.
关键词：
Multiplicity;Degenerate Kirchhoff type equation;Critical growth;Variational method
摘要：
In this paper, we study the following Kirchhoff type problem with critical growth {-M (integral(Omega)vertical bar del u vertical bar(2)dx) Delta u = lambda vertical bar u vertical bar(2)u + vertical bar u vertical bar(4)u in Omega, u = 0, on partial derivative Omega, where Omega is a smooth bounded domain in R-3, M is an element of C(R+, R) and lambda > 0. We prove the existence of multiple nontrivial solutions for the above problem, when parameter lambda belongs to some left neighborhood of the eigenvalue of the nonlinear operator -M(integral(Omega) vertical bar del u vertical bar(2) dx)Delta. (C) 2017 Elsevier Ltd. All rights reserved.
摘要：
In this paper, we discuss the properties of simple modules over Auslander regular rings with global dimension at most 3. Using grade theory, we show the right projective dimension of ExtΛ1(S,Λ) is equal to 1 for any simple Λ-module S with gr S = 1. As a result, we give some equivalent characterization of diagonal Auslander regular rings.
摘要：
This paper deals with a stochastic two-species competitive model. Some very verifiable criteria on the global stability of the positive equilibrium of the deterministic system are established. An example with its computer simulations is given to illustrate our main theoretical findings.
作者机构：
[Guo, Ping; Sun, Xiao-Dong] Univ South China, Sch Math & Phys, Hengyang 421001, Peoples R China.;[Li, Xiao-Hua; Xiang, Dong; Deng, Jun-Gang] Univ South China, Sch Nucl Sci & Technol, Hengyang 421001, Peoples R China.;[Li, Xiao-Hua] Univ South China, Cooperat Innovat Ctr Nucl Fuel Cycle Technol & Eq, Hengyang 421001, Peoples R China.;[Li, Xiao-Hua] Hunan Normal Univ, Key Lab Low Dimens Quantum Struct & Quantum Contr, Changsha 410081, Hunan, Peoples R China.
通讯机构：
[Xiang, Dong] U;Univ South China, Sch Nucl Sci & Technol, Hengyang 421001, Peoples R China.
摘要：
α decay is a common and important process of natural radioactivity of the heavy and superheavy nuclei. From the α decay of nuclei, we can obtain much more information of nuclei structure. In our previous works [X.-D. Sun et al., Phys. Rev. C 93, 034316 (2016); X.-D. Sun et al., Phys. Rev. C 95, 014319 (2017)], we have done systematic study on the α preformation probability of both the even-even and odd- A nuclei within the two-potential approach. The α preformation probabilities will systematically change due to the shell effect, proton-neutron correlation, and so on. This work is the extension of the previous works. In this work, we systematically study the α decay of doubly odd nuclei. We find that for superallowed α decay the α preformation probabilities of doubly odd nuclei are larger than those of odd- A ones in general, and for the heavier nuclei the extra neutrons suppress the proton-neutron correlation resulting in the small α preformation probabilities. The calculated results can well reproduce the experimental half-lives. The half-lives of the α decay chain beginning from nuclide 119296 are also predicted and compared with various empirical formulas.
期刊：
Nonlinear Analysis: Real World Applications,2017年36:116-138 ISSN：1468-1218
通讯作者：
Guo, Shangjiang
作者机构：
[Liu, Zhisu] Univ South China, Sch Math & Phys, Hengyang 421001, Hunan, Peoples R China.;[Guo, Shangjiang] Hunan Univ, Coll Math & Econometr, Changsha 410082, Hunan, Peoples R China.;[Zhang, Ziheng] Tianjin Polytech Univ, Dept Math, Tianjin 300387, Peoples R China.
通讯机构：
[Guo, Shangjiang] H;Hunan Univ, Coll Math & Econometr, Changsha 410082, Hunan, Peoples R China.
关键词：
Generalized Nehari manifold;Ground state;Homoclinic orbit;Second-order Hamiltonian system
摘要：
We deal with the following second-order Hamiltonian systems u - L(t)u + del W (t, u) = 0, where L is an element of C(R,R-N2) is a symmetric and positive define matrix for all t is an element of R, W is an element of C-1 (R x R-N, R) and del W(t, u) is the gradient of W with respect to u. Under the superquadratic condition, we obtain the existence of ground state homoclinic orbits by means of the generalized Nehari manifold developed by Szulkin and Weth. Under the subquadratic condition, we employ variational techniques and the concentration-compactness principle to establish new criteria guaranteeing the multiplicity of classical homoclinic orbits. Recent results in literature are generalized and significantly improved. (C)2017 Elsevier Ltd. All rights reserved.
作者机构：
[Li, Zhenbo] Univ South China, Sch Math & Phys, Hengyang 421001, Peoples R China.;[Tang, Jiashi] Hunan Univ, Coll Mech & Vehicle Engn, Changsha 410082, Hunan, Peoples R China.
通讯机构：
[Li, Zhenbo] U;Univ South China, Sch Math & Phys, Hengyang 421001, Peoples R China.
关键词：
Generalized binary function projective synchronization;Special matrix structure;Adaptive control
摘要：
Based on function projective synchronization theorem, a novel type of synchronization scheme called generalized binary function projective synchronization is proposed. Combining adaptive control theory with special matrix structure, an extended adaptive controller which is more general than some existing controllers is designed. Under the controller, the proposed synchronization between two different uncertain chaotic systems is achieved and the unknown parameters are also estimated. Numerical simulation result is presented to show the validity and feasibility of the scheme and controller. (C) 2017 Elsevier GmbH. All rights reserved.
摘要：
Fast wave in the ion-cyclotron resonance frequency (ICRF) range is a promising candidate for non-inductive current drive (CD), which is essential for long pulse and high performance operation of tokamaks. A numerical study on the ICRF fast wave current drive (FWCD) and mode-conversion current drive (MCCD) in the Experimental Advanced Superconducting Tokamak (EAST) is carried out by means of the coupled full wave and Ehst-Karney parameterization methods. The results show that FWCD efficiency is notable in two frequency regimes, i.e., f ≥ 85 MHz and f = 50–65 MHz, where ion cyclotron absorption is effectively avoided, and the maximum on-axis driven current per unit power can reach 120 kA/MW. The sensitivity of the CD efficiency to the minority ion concentration is confirmed, owing to fast wave mode conversion, and the peak MCCD efficiency is reached for 22% minority-ion concentration. The effects of the wave-launch position and the toroidal wavenumber on the efficiency of current drive are also investigated.
