Multiple positive solutions of nonlinear singular m-point boundary value problem for second-order dynamic equations with sign changing coefficients on time scales

Let $\mathbb{T}$ be a time scale. In this paper, we study the existence of multiple positive solutions for the following nonlinear singular $m$-point boundary value problem dynamic equations with sign changing coefficients on time scales $$\left\{\begin{array}{lll} u^{\triangle\nabla}(t)+ a(t)f(u(t))=0, (0,T)_{\mathbb{T}}, \cr\ u^{\triangle}(0)=\sum_{i=1}^{m-2}a_{i}u^{\triangle}(\xi_i), \cr u(T)=\sum_{i=1}^{k}b_{i}u(\xi_i)-\sum_{i=k+1}^{s}b_{i}u(\xi_i)-\sum_{i=s+1}^{m-2}b_{i}u^{\triangle}(\xi_i), \end{array}\right.$$ where $1\leq k\leq s\leq m-2, a_i, b_i\in(0,+\infty)$ with $0<\sum_{i=1}^{k}b_{i}-\sum_{i=k+1}^{s}b_{i}<1, 0<\sum_{i=1}^{m-2}a_{i}<1, 0<\xi_1<\xi_2<\cdots<\xi_{m-2}<\rho(T)$, $f\in C( [0,+\infty),[0,+\infty))$, $a(t)$ may be singular at $t=0$. We show that there exist two positive solutions by using two different fixed point theorems respectively. As an application, some examples are included to illustrate the main results. In particular, our criteria extend and improve some known results

Three symmetric positive solutions of fourth-order singular nonlocal boundary value problems

In this paper, we study the existence of three positive solutions of fourth-order singular nonlocal boundary value problems. We show that there exist triple symmetric positive solutions by using Leggett-Williams fixed-point theorem. The conclusions in this paper essentially extend and improve some known results

Flat bands and magnetism in Fe4GeTe2\mathrm{Fe_4 Ge Te_2} and Fe5GeTe2\mathrm{Fe_5GeTe_2} due to bipartite crystal lattices

$\mathrm{Fe_{n=4,5}GeTe_2}$ exhibits quasi-two-dimensional properties as a promising candidate for a near-room-temperature ferromagnet, which has attracted great interest. In this work, we notice that the crystal lattice of $\mathrm{Fe_{n=4,5}GeTe_2}$ can be approximately considered to be stacked by three bipartite crystal lattices. By combining the model Hamiltonians of bipartite crystal lattices and first-principles calculations, we investigate the electronic structure and the magnetism of $\mathrm{Fe_{n=4,5}GeTe_2}$. We conclude that flat bands near the Fermi level originate from the bipartite crystal lattices and that these flat bands are expected to lead to the itinerant ferromagnetism in $\mathrm{Fe_{n=4,5}GeTe_2}$. Interestingly, we also find that the magnetic moment of the Fe5 atom in $\mathrm{Fe_5 Ge Te_2}$ is distinct from the other Fe atoms and is sensitive with the Coulomb interaction $U$ and external pressure. These findings may be helpful to understand the exotic magnetic behavior of $\mathrm{Fe_{n=4,5} Ge Te_2}$.Comment: 9 pages, 8 figure

Multiple symmetric nonnegative solutions of second-order ordinary differential equations

AbstractThe existence of multiple nonnegative solutions of the equations −χ″ = f(χ, χ′) subject to χ(0) = χ(1) = 0 is studied. The result is obtained that there are at least three symmetric nonnegative solutions if certain conditions are imposed on f

Methane activation by nickel cluster cations, Nin+ (n=2-16): reaction mechanisms and thermochemistry of cluster-CHx (x=0-3) complexes

Journal ArticleThe kinetic energy dependences of the reactions of Nin+ (n=2-16) with CD4 are studied in a guided ion beam tandem mass spectrometer over the energy range of 0-10 eV. The main products are hydride formation NinD1, dehydrogenation to form NinCD2 1 , and double dehydrogenation yielding NinC1

Guided ion-beam studies of the reactions of Con + (n=2-20) with O2: cobalt cluster-oxide and -dioxide bond energies

Journal ArticleThe kinetic-energy dependence for the reactions of Con + (n=2-20) with O2 is measured as a function of kinetic energy over a range of 0 to 10 eV in a guided ion-beam tandem mass spectrometer. A variety of Com+ , ComO+, and ComO2 + (m<n) product ions is observed, with the dioxide cluster ions dominating the products for all larger clusters. Reaction efficiencies of Con+ cations with O2 are near unity for all but the dimer

The Effects Of Orography On Wind, Cloud, And Rainfall Patterns During Typhoon Ketsana (2009)

Understanding the orographic effect is crucial for both disaster prevention and weather prediction for events such as tropical cyclones (TCs). Because of the complexity of orographic effects, due to the presence of mountains, the influence of orography on TCs remains unclear and is an active area of scientific research. The objective of this study is to investigate the effects of orography on the rainfall, wind, and cloud systems of the TCs in Malaysia, as this type of study has never been performed in Malaysia

Positive Solutions for Third-Order Nonlinear p

We study the following third-order p-Laplacian m-point boundary value problems on time scales: (ϕp(uΔ∇))∇+a(t)f(t,u(t))=0, t∈[0,T]T, βu(0)−γuΔ(0)=0, u(T)=∑i=1m−2aiu(ξi), ϕp(uΔ∇(0))=∑i=1m−2biϕp(uΔ∇(ξi)), where ϕp(s) is p-Laplacian operator, that is, ϕp(s)=|s|p−2s, p>1,  ϕp−1=ϕq, 1/p+1/q=1,  0<ξ1<⋯<ξm−2<ρ(T). We obtain the existence of positive solutions by using fixed-point theorem in cones. The conclusions in this paper essentially extend and improve the known results