Existence and Multiplicity of Solutions for a Class of Elliptic Equations Without Ambrosetti–Rabinowitz Type Conditions

In this paper we establish, using variational methods, the existence and multiplicity of weak solutions for a general class of quasilinear problems involving \(p(\cdot )\)-Laplace type operators, with Dirichlet boundary conditions involving variable exponents without Ambrosetti and Rabinowitz (A-R) type growth conditions, namely

$$\begin{aligned} \left\{ \begin{array}{rcll} -{\text {div}}(a(|\nabla u|^{p(x)})|\nabla u|^{p(x)-2}\nabla u)&{}=&{}\lambda f(x,u) &{} \text{ in } \Omega ,\\ u&{}=&{}0 &{} \text{ on } \partial \Omega . \end{array} \right. \end{aligned}$$

By different types of versions of the Mountain Pass Theorem with Cerami condition, as well as, the Fountain and Dual Theorem with Cerami condition, we obtain some existence of weak solutions for the above problem under some considerations. Moreover, we show that the problem treated has at least one nontrivial solution for any parameter \(\lambda >0\) small enough, and also that the solution blows up, in the Sobolev norm, as \(\lambda \rightarrow 0^{+}.\) Finally, by imposing additional hypotheses on the nonlinearity \(f(x,\cdot ),\) we get the existence of infinitely many weak solutions by using the Genus Theory introduced by Krasnoselskii.

     

用正电子寿命谱研究GeSe_x硫系玻璃的自由体积

采用正电子寿命谱和拉曼散射研究了不同组分配比的Ge Sex(x=6,7,8,9)硫系玻璃的微结构.正电子寿命结果显示在x=8时,其平均正电子寿命具有最小值.拉曼光谱结果研究表明,这种硫系玻璃样品主要由[Ge Se4]四面体和Seμ链的结构单元构成.以上的实验结果用级配理论得到了合理的解释,这两种结构单元配比关系的变化导致硫系玻璃样品中的自由体积变化,从而导致正电子平均寿命减小.研究发现Ge Se8具有最小的自由体积,即具有最稳定的结构.     

双钙态矿Sr_2Fe_(1-x)Mn_xMoO_6体系的磁性和磁输运性质的研究(英文)

我们用X射线光电子能谱、以及相关的电性和磁性测量研究了Sr2Fe1-xMnxMoO6(0相似文献   

以“问题”为主线的多元化教学方法和模式的研究

简要介绍了在物理实验的"教"与"学"过程中,改变教学模式,以"问题"为主线,开展多元化的教学方法和模式. 实践表明,该教学模式促进了学生自主创新意识和综合实验研究能力的提升.     

阴离子分散剂对酸化膨润土流变性的影响

研究了阴离子分散剂聚丙烯酸钠对质量分数为10%的酸化膨润土分散体系流变性的影响. 结果表明, 添加0.4%分散剂的分散体系的剪切应力、表观黏度和屈服应力最低. 其它体系流体均表现为从假塑型到胀流型流体的转变, 而含0.4%分散剂的体系始终表现为胀流型流体. 采用Herschel-Bulkley模型对各体系的流变曲线进行了拟合, 得到较好的拟合曲线, 同时探讨了酸化膨润土分散体系的流变机理.     

PH_3配体在团簇Au_(20)的顶点和面心配位的DFT理论研究

采用DFT方法研究了在团簇Au20的顶端位点和面心位点配位PH3分子时的几何结构、电子结构以及Au-P的成键机理和能量分析.在两种配位方式下,配体PH3对团簇的几何结构影响都表现为强烈的局域形变效应.不同的配位方式下PH3与团簇的轨道作用方式不同,所形成的团簇化合物电子组态不同.两种配位方式下Au-P成键能的区别主要是来自于配体与团簇之间的Pauli排斥的不同,在面心配位时配体与团簇之间更大的Pauli排斥作用导致了该配位方式的不稳定.     

Chromium(III) complexes with terdentate 2,6-bis(azolylmethyl)pyridine ligands: Synthesis, structures and ethylene polymerization behavior

Reactions of 2,6-bis(bromomethyl)pyridine with 3,5-dimethylpyrazole and 1H-indazole yield the terdentate ligands 2,6-bis(3,5-dimethylpyrazol-1-ylmethyl)pyridine (5) and 2,6-bis(indazol-2-ylmethyl)pyridine (6). The molecular structure of the new compound 6 was determined by single-crystal X-ray diffraction. These ligands react with the CrCl₃(THF)₃ complex in THF to form neutral complexes of general formula [CrCl₃{2,6-bis(azolylmethyl)pyridine-N,N,N}] (7, 8) which are isolated in high yields as stable green solids and characterized by means of elemental analysis, magnetic moments, IR, and mass spectroscopy. Theoretical calculations predict that the thermodynamically preferred structure of the complexes is the fac configuration. After reaction with methylaluminoxane (MAO) the chromium(III) complexes are active in the polymerization of ethylene.     

Matching Points with Squares

Given a class of geometric objects and a point set P, a -matching of P is a set of elements of such that each C _i contains exactly two elements of P and each element of P lies in at most one C _i . If all of the elements of P belong to some C _i , M is called a perfect matching. If, in addition, all of the elements of M are pairwise disjoint, we say that this matching M is strong. In this paper we study the existence and characteristics of -matchings for point sets in the plane when is the set of isothetic squares in the plane. A consequence of our results is a proof that the Delaunay triangulations for the L _∞ metric and the L ₁ metric always admit a Hamiltonian path.     

A Polynomial Bound for Untangling Geometric Planar Graphs

To untangle a geometric graph means to move some of the vertices so that the resulting geometric graph has no crossings. Pach and Tardos (Discrete Comput. Geom. 28(4): 585–592, 2002) asked if every n-vertex geometric planar graph can be untangled while keeping at least n ^ε vertices fixed. We answer this question in the affirmative with ε=1/4. The previous best known bound was \(\Omega(\sqrt{\log n/\log\log n})\). We also consider untangling geometric trees. It is known that every n-vertex geometric tree can be untangled while keeping at least \(\Omega(\sqrt{n})\) vertices fixed, while the best upper bound was \(\mathcal{O}((n\log n)^{2/3})\). We answer a question of Spillner and Wolff (http://arxiv.org/abs/0709.0170) by closing this gap for untangling trees. In particular, we show that for infinitely many values of n, there is an n-vertex geometric tree that cannot be untangled while keeping more than \(3(\sqrt{n}-1)\) vertices fixed.     

Analysis of Low-polar Ginsenosides in Steamed Panax Ginseng at High-temperature by HPLC-ESI-MS/MS

A high performance liquid chromatography coupled with electrospray ionization-tandem mass spectrometry( HPLC-ESI-MS/MS) method was developed for the analysis and identification of ginsenosides in the extracts of raw Panax ginseng(RPG) and steamed Panax ginseng at high temperatures(SPGHT). A total of 25 ginsenosides were extracted include of which 10 low-polar ginsenosides, such as ginsenosides F4, Rk3, Rh4, 20S-Rg3, 20R-Rg3 and so on, were identified according to their HPLC retention time and MS/MS data. The results indicated that the low polar ginsenosides were seldom found in RPG. For the exploration of the transformation pattern of the ginsenosides in steam processing, the standards of ginsenosides Re, Rg1, Rb1, Rc, Rb2, Rb3 and Rd were selected and hydrolyzed at a temperature of 120 ℃. The results show that these polar ginsenosides can be converted to low-polar ginsenosides such as Rg2, Rg6, F4, Rk3 and Rg5 by hydrolyzing the sugar chains.