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

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

The Existence of Positive Solutions for an Integral Boundary Value Problems

In this paper, by using fixed point theorem of cone expansion-compression type and suitable conditions, we present the existence of single positive solution for the integral boundary value problems. We derive an explicit interval of λ such that for any λ in this interval, the existence of at least one positive solution to the boundary value problems is guaranteed

Deciphering of interactions between platinated DNA and HMGB1 by hydrogen/deuterium exchange mass spectrometry

A high mobility group box 1 (HMGB1) protein has been reported to recognize both 1,2-intrastrand crosslinked DNA by cisplatin (1,2-cis-Pt-DNA) and monofunctional platinated DNA using trans-[PtCl2(NH3)(thiazole)] (1-trans-PtTz-DNA). However, the molecular basis of recognition between the trans-PtTz-DNA and HMGB1 remains unclear. In the present work, we described a hydrogen/deuterium exchange mass spectrometry (HDX-MS) method in combination with docking simulation to decipher the interactions of platinated DNA with domain A of HMGB1. The global deuterium uptake results indicated that 1-trans-PtTz-DNA bound to HMGB1a slightly tighter than the 1,2-cis-Pt-DNA. The local deuterium uptake at the peptide level revealed that the helices I and II, and loop 1 of HMGB1a were involved in the interactions with both platinated DNA adducts. However, docking simulation disclosed different H-bonding networks and distinct DNA-backbone orientations in the two Pt-DNA-HMGB1a complexes. Moreover, the Phe37 residue of HMGB1a was shown to play a key role in the recognition between HMGB1a and the platinated DNAs. In the cis-Pt-DNA-HMGB1a complex, the phenyl ring of Phe37 intercalates into a hydrophobic notch created by the two platinated guanines, while in the trans-PtTz-DNA-HMGB1a complex the phenyl ring appears to intercalate into a hydrophobic crevice formed by the platinated guanine and the opposite adenine in the complementary strand, forming a penta-layer π–π stacking associated with the adjacent thymine and the thiazole ligand. This work demonstrates that HDX-MS associated with docking simulation is a powerful tool to elucidate the interactions between platinated DNAs and proteins

Candidate Regulators of Dyslipidemia in Chromosome 1 Substitution Lines Using Liver Co-Expression Profiling Analysis

Dyslipidemia is a major risk factor for cardiovascular disease. Although many genetic factors have been unveiled, a large fraction of the phenotypic variance still needs further investigation. Chromosome 1 (Chr 1) harbors multiple gene loci that regulate blood lipid levels, and identifying functional genes in these loci has proved challenging. We constructed a mouse population, Chr 1 substitution lines (C1SLs), where only Chr 1 differs from the recipient strain C57BL/6J (B6), while the remaining chromosomes are unchanged. Therefore, any phenotypic variance between C1SLs and B6 can be attributed to the differences in Chr 1. In this study, we assayed plasma lipid and glucose levels in 13 C1SLs and their recipient strain B6. Through weighted gene co-expression network analysis of liver transcriptome and "guilty-by-association" study, eight associated modules of plasma lipid and glucose were identified. Further joint analysis of human genome wide association studies revealed 48 candidate genes. In addition, 38 genes located on Chr 1 were also uncovered, and 13 of which have been functionally validated in mouse models. These results suggest that C1SLs are ideal mouse models to identify functional genes on Chr 1 associated with complex traits, like dyslipidemia, by using gene co-expression network analysis

Existence and Iteration of Positive Solutions for Multipoint Boundary Value Problems Dependence on the First Order Derivative with One-Dimensional p-Laplacian

Abstract In this paper, we study the existence of monotone positive solutions for the following nonlinear m-point singular boundary value problem with p-Laplacian operator. The main tool is the monotone iterative technique. We obtain not only the existence of positive solutions for the problem, but also establish iterative schemes for approximating solution. Mathematics Subject Classification: 34B1