Some New Existence Results of Positive Solutions to an Even-Order Boundary Value Problem on Time Scales

We consider a high-order three-point boundary value problem. Firstly, some new existence results of at least one positive solution for a noneigenvalue problem and an eigenvalue problem are established. Our approach is based on the application of three different fixed point theorems, which have extended and improved the famous Guo-Krasnosel'skii fixed point theorem at different aspects. Secondly, some examples are included to illustrate our results

Two-dimensional spin liquid behaviour in the triangular-honeycomb antiferromagnet TbInO₃

Spin liquid ground states are predicted to arise within several distinct scenarios in condensed matter physics. The observation of these disordered magnetic states is particularly pervasive among a class of materials known as frustrated magnets, in which the competition between various magnetic exchange interactions prevents the system from adopting long-range magnetic order at low temperatures. Spin liquids continue to be of great interest due to their exotic nature and the possibility that they may support fractionalized excitations, such as Majorana fermions. Systems that allow for such phenomena are not only fascinating from a fundamental perspective but may also be practically significant in future technologies based on quantum computation. Here we show that the underlying antiferromagnetic sublattice in TbInO3 can undergo a crystal field-induced distortion of its buckled triangular arrangement to one based on a honeycomb. The absence of a conventional magnetic ordering transition at the lowest measurable temperatures indicates that another critical mechanism must govern in the ground-state selection of TbInO3. We suggest that anisotropic exchange interactions—mediated through strong spin–orbit coupling on the emergent honeycomb lattice of TbInO3—give rise to a highly frustrated spin liquid

New genetic loci link adipose and insulin biology to body fat distribution.

Body fat distribution is a heritable trait and a well-established predictor of adverse metabolic outcomes, independent of overall adiposity. To increase our understanding of the genetic basis of body fat distribution and its molecular links to cardiometabolic traits, here we conduct genome-wide association meta-analyses of traits related to waist and hip circumferences in up to 224,459 individuals. We identify 49 loci (33 new) associated with waist-to-hip ratio adjusted for body mass index (BMI), and an additional 19 loci newly associated with related waist and hip circumference measures (P < 5 × 10(-8)). In total, 20 of the 49 waist-to-hip ratio adjusted for BMI loci show significant sexual dimorphism, 19 of which display a stronger effect in women. The identified loci were enriched for genes expressed in adipose tissue and for putative regulatory elements in adipocytes. Pathway analyses implicated adipogenesis, angiogenesis, transcriptional regulation and insulin resistance as processes affecting fat distribution, providing insight into potential pathophysiological mechanisms

Successive Iteration and Positive Solutions for Nonlinear m-Point Boundary Value Problems on Time Scales

We study the existence of positive solutions for a class of m-point boundary value problems on time scales. Our approach is based on the monotone iterative technique and the cone expansion and compression fixed point theorem of norm type. Without the assumption of the existence of lower and upper solutions, we do not only obtain the existence of positive solutions of the problem, but also establish the iterative schemes for approximating the solutions

Sign-Changing Solutions for Nonlinear Operator Equations

The existence of six solutions for nonlinear operator equations is obtained by using the topological degree and fixed point index theory. These six solutions are all nonzero. Two of them are positive, the other two are negative, and the fifth and sixth ones are both sign-changing solutions. Furthermore, the theoretical results are applied to elliptic partial differential equations

Positive solutions for nonlinear difference equations involving the p-Laplacian with sign changing nonlinearity

By means of fixed point index, we establish sufficient conditions for the existence of positive solutions to p-Laplacian difference equations. In particular, the nonlinear term is allowed to change sign

Nonlinear sum operator equations and applications to elastic beam equation and fractional differential equation

Abstract In this paper, by studying the solutions of the abstract operator equation A(x,x)+B(x,x)+e=x $A(x,x)+B(x,x)+e=x$ on ordered Banach spaces, where A, B are two mixed monotone operators and e∈P $e\in P$ with θ≤e≤h $\theta \leq e\leq h$, we prove a class of boundary value problems on elastic beam equation to have a unique solution. Furthermore, we also apply our abstract result to establish the existence and uniqueness theorem of nontrivial solutions for nonlinear fractional boundary value problems. The iterative sequences to approximate unique solutions for the above two classes of problems are also obtained

An exact estimate result for p-biharmonic equations with Hardy potential and negative exponents

Abstract In this paper, p-biharmonic equations involving Hardy potential and negative exponents with a parameter λ are considered. By means of the structure and properties of Nehari manifold, we give uniform lower bounds for Λ>0 $\varLambda >0$, which is the supremum of the set of λ. When λ∈(0,Λ) $\lambda \in (0, \varLambda )$, the above problems admit at least two positive solutions