On existence and uniqueness of positive solutions for integral boundary boundary value problems

By applying the monotone iterative technique, we obtain the existence and uniqueness of $C^1[0,1]$ positive solutions in some set for singular boundary value problems of second order ordinary differential equations with integral boundary conditions

Laplace’s equation with concave and convex boundary nonlinearities on an exterior region

Abstract This paper studies Laplace’s equation −Δu=0 $-\Delta u=0$ in an exterior region U⊊RN $U\varsubsetneq {\mathbb{R}}^{N}$, when N≥3 $N\geq 3$, subject to the nonlinear boundary condition ∂u∂ν=λ|u|q−2u+μ|u|p−2u $\frac{\partial u}{\partial \nu }=\lambda \vert u \vert ^{q-2}u+\mu \vert u \vert ^{p-2}u$ on ∂U with 10 $\lambda >0$ and μ∈R $\mu \in \mathbb{R}$ arbitrary, then there exists a sequence {uk} $\{u_{k} \}$ of solutions with negative energy converging to 0 as k→∞ $k\to \infty$; on the other hand, when λ∈R $\lambda \in \mathbb{R}$ and μ>0 $\mu >0$ arbitrary, then there exists a sequence {u˜k} $\{\tilde{u}_{k} \}$ of solutions with positive and unbounded energy. Also, associated with the p-Laplacian equation −Δpu=0 $-\Delta _{p} u=0$, the exterior p-harmonic Steklov eigenvalue problems are described

A Fixed-Point Theorem for Ordered Contraction-Type Decreasing Operators in Banach Space with Lattice Structure

In this work, we mainly improve the results in Amini-Harandi and Emami (2010). By introducing a new kind of ordered contraction-type decreasing operator in Banach space, we obtain a unique fixed point by using the iterative algorithm. An example is also presented to illustrate the theorem

TFRC in cardiomyocytes promotes macrophage infiltration and activation during the process of heart failure through regulating Ccl2 expression mediated by hypoxia inducible factor‐1α

Abstract Background Cardiac hypertrophy is an initiating link to Heart failure (HF) which still seriously endangers human health. Transferrin receptor (TFRC), which promotes iron uptake through the transferrin cycle, is essential for cardiac function. However, whether TFRC is involved in the process of pathological cardiac hypertrophy is not clear. Methods Transverse aortic constriction (TAC) mouse model and mice primary cardiomyocytes treated with isoproterenol (ISO) or phenylephrine (PHE) were used to mimic cardiac hypertrophy in vivo and in vitro. Single cell RNA sequence data from heart tissues of TAC‐model mice was obtained from the Gene Expression Omnibus (GEO) database, and was analyzed with R package Seurat. TFRC expression and macrophage infiltration in the heart tissue were tested by immunofluorescent staining. Macrophage polarization was detected by Flow Cytometry. TFRC expressions were detected by qRT‐PCR, Western blot, and ELISA. Results TFRC expression is increased in the pathological cardiac hypertrophy of mice model and positively associated with macrophage infiltration. Furthermore, TFRC in cardiomyocytes recruits and activates macrophages by secreting C‐C motif ligand 2 (Ccl2) in the mice heart tissue with TAC surgery or in the primary cardiomyocytes stimulated with ISO or PHE to induce myocardial hypertrophy in vitro. Moreover, we find that TFRC promotes Ccl2 expression in cardiomyocytes via regulating signal transducer and activator of transcription 3 (STAT3). In addition, we find that increased TFRC expression in the HF tissue is regulated by hypoxia‐inducible factor‐1α (HIF‐1α). Conclusion This in‐depth study shows that TFRC in cardiomyocytes promotes HF development through inducing macrophage infiltration and activation via the STAT3‐Ccl2 signaling, and TFRC expression in cardiomyocytes is regulated by HIF‐1α during HF. This study first uncovers the role of TFRC in cardiomyocytes on macrophage infiltration and activation during HF