Variational approaches to impulsive elastic beam equations of Kirchhoff type

In this paper, we study the existence of multiple solutions for impulsive fourth-order differential equations of Kirchhoff type. Using a variational method and some critical points theorems, we obtain some new criteria for guaranteeing that impulsive fourth-order differential equations of Kirchhoff type have three and infinitely many solutions. Some recent results are extended and improved. Some examples are presented to demonstrate the applications of our main results.     

雾化角对液体火箭发动机燃烧室压力振荡的影响

针对液氧/煤油火箭发动机模型燃烧室实现了三维非稳态两相燃烧过程的数值模拟,得到的燃烧室截面平均压力和平均速度与实验吻合。在初边值条件不施加任何扰动的情况下,得到了燃烧室压力自激振荡过程,并研究了液氧和煤油喷嘴雾化角对燃烧室压力振荡的影响。计算结果表明:当雾化角为40°或120°时,由于燃料与氧化剂喷雾锥重叠区域较小或较大,导致了推进剂混合很差或很好,不易在燃烧室头部出现局部爆炸性的可燃混气团,致使燃烧室压力振荡强度较弱;而当雾化角为中间值65°时,易于出现爆炸性的可燃气团并导致剧烈的压力振荡,使燃烧室中出现燃烧不稳定性。因此,雾化角的合理设计是抑制燃烧不稳定性的一种途径。     

内蒙古地区沙生植物--沙枣中维生素C含量的测定

在 pH 6.0的 HAc-NaAc缓冲溶液中,用活性炭吸附沙枣中的色素,Cu(Ⅱ)催化氧化维生素C,在λmax=268 nm处可直接测定沙枣中维生素C含量.与传统碘量法相比,测定结果基本一致.为内蒙古地区沙枣天然植物资源的药用开发、食品加工等提供了参考数据.     

Laser Diode-Pumped Nd：LuVO4 Acousto-Optic Q-Switched Laser at 916 nm

A compact laser diode-pumped solid-state Nd：LuVO4 acousto-optic Q-switched laser is demonstrated at 916 nm of a quasi-three level for the first time. A pulse width of 130ns is observed when the pulse-repetition frequency is 10 kHz. The laser experiment shows that the Nd：Lu VO4 crystal can be used for efficient diode-pumped Q-switched lasers.     

Theoretical study of H⋯P and X⋯P interactions of methylphosphines with HSX molecules

Ab initio calculations were used to analyze the interactions between thiohypohalous acids (HSX; X = F, Cl, Br, I) and methylphosphine derivatives (PH _n Me_3?n , n = 0–3) at the MP2/aug-cc-pVDZ level of theory. Interaction of HSX with PH _n Me_3?n leads to both hydrogen bond (HSX–PH _n Me_3?n –HB) as well as halogen bond (HSX–PH _n Me_3?n –XB) complexes. Stabilities of both HB and XB complexes increase with basicity of the phosphines. However, HB complexes of a phosphine molecule with different HSX have the same order of stabilities, but XB complexes of heavier thiohypohalous acids are more stable. Electron densities of complexes were characterized with the atoms in molecules methodology. The charge transfer within dimers was analyzed by means of natural bond orbitals.     

Infinitely many solutions for Steklov problems associated to non-homogeneous differential operators through Orlicz-Sobolev spaces

Employing variational methods and critical point theory, in an appropriate Orlicz-Sobolev setting, we establish the existence of infinitely many solutions for Steklov problems associated to non-homogeneous differential operators. We also provide some particular cases and a concrete example in order to illustrate the main results.     

Existence results for a class of degenerate quasilinear elliptic systems

We establish existence results for weak solutions of degenerate quasilinear elliptic systems. By using the variational method we obtain the existence of a solution for an elliptic system with Dirichlet boundary condition under some restriction on λ.     

On Some Quasilinear Elliptic Systems with Singular and Sign-Changing Potentials

Using variational methods, we study the existence and nonexistence of nontrivial weak solutions for the quasilinear elliptic system $$\left\{\begin{array}{ll}- {\rm div}(h_1(|\nabla u|^2)\nabla u) = \frac{\mu}{|x|^2}u + \lambda F_u(x, u, \upsilon)\quad {\rm in}\,\Omega,\\- {\rm div}(h_2(|\nabla \upsilon|^2)\nabla \upsilon) = \frac{\mu}{|x|^2}\upsilon + \lambda F_\upsilon(x,u,\upsilon)\quad {\rm in}\,\Omega,\\u = \upsilon = 0 \qquad \qquad \qquad \qquad \qquad \qquad {\rm in}\, \partial\Omega, \end{array}\right.$$ where \({\Omega \subset \mathbb{R}^N,N \geq 3}\) , is a bounded domain containing the origin with smooth boundary \({\partial \Omega ; h_i, i = 1, 2}\) , are nonhomogeneous potentials; \({(F_u, F_v) = \nabla F}\) stands for the gradient of a sign-changing C ¹-function \({F : \Omega \times \mathbb{R}^2 \to \mathbb{R}}\) in the variable \({{w = (u, v) \in \mathbb{R}^2}}\) ; and λ and μ are parameters.