On the existence and properties of three types of solutions of singular IVPs

The paper studies the singular initial value problem (p(t)u 0 (t))0 + q(t)f(u(t)) = 0, t > 0, u(0) = u0 ∈ [L0, L] , u 0 (0) = 0. Here, f ∈ C(R), f(L0) = f(0) = f(L) = 0, L0 0 for x ∈ (L0, 0) ∪ (0, L). Further, p, q ∈ C [ 0, ∞ ) are positive on (0, ∞) and p(0) = 0. The integral R 1 0 ds p(s) may be divergent which yields the time singularity at t = 0. The paper describes a set of all solutions of the given problem. Existence results and properties of oscillatory solutions and increasing solutions are derived. By means of these results, the existence of an increasing solution with u(∞) = L (a homoclinic solution) playing an important role in applications is proved.Web of Scienceno. 2925

On the existence and properties of three types of solutions of singular IVPs

The paper studies the singular initial value problem $$(p(t)u'(t))' + q(t)f(u(t))=0, \qquad t>0, \qquad u(0)=u_0\in [L_0,L], \qquad u'(0)=0.$$ Here, $f\in C(\mathbb{R})$, $f(L_0)=f(0)=f(L)=0$, $L_0 < 0 < L$ and $xf(x)>0$ for $x\in (L_0,0) \cup (0,L)$. Further, $p,q\in C[0,\infty)$ are positive on $(0,\infty)$ and $p(0)=0$. The integral $\int_0^1 \frac{\mathrm{d}{s}}{p(s)}$ may be divergent which yields the time singularity at $t=0$. The paper describes a set of all solutions of the given problem. Existence results and properties of oscillatory solutions and increasing solutions are derived. By means of these results, the existence of an increasing solution with $u(\infty)=L$ (a homoclinic solution) playing an important role in applications, is proved

Existence and uniqueness of damped solutions of singular IVPs with phi-Laplacian

We study analytical properties of a singular nonlinear ordinary differential equation with a phi-Laplacian. In particular we investigate solutions of the initial value problem (p(t)phi(u'(t)))' + p(t)f(phi(u(t))) = 0, u(0) = u(0) is an element of [L-0, L], u'(0) = 0 on the half-line [0, infinity). Here, f is a continuous function with three zeros phi(L0) < 0 < phi(L), function p is positive on (0, infinity) and the problem is singular in the sense that p(0) - 0 and 1/p(t) may not be integrable on [0,1]. The main goal of the paper is to prove the existence of damped solutions defined as solutions u satisfying sup{u(t), t is an element of [0, infinity)} < L. Moreover, we study the uniqueness of damped solutions. Since the standard approach based on the Lipschitz property is not applicable here in general, the problem is more challenging. We also discuss the uniqueness of other types of solutions.Web of Science12128

Health and Disease—Emergent States Resulting From Adaptive Social and Biological Network Interactions

Health is an adaptive state unique to each person. This subjective state must be distinguished from the objective state of disease. The experience of health and illness (or poor health) can occur both in the absence and presence of objective disease. Given that the subjective experience of health, as well as the finding of objective disease in the community, follow a Pareto distribution, the following questions arise: What are the processes that allow the emergence of four observable states—(1) subjective health in the absence of objective disease, (2) subjective health in the presence of objective disease, (3) illness in the absence of objective disease, and (4) illness in the presence of objective disease? If we consider each individual as a unique biological system, these four health states must emerge from physiological network structures and personal behaviors. The underlying physiological mechanisms primarily arise from the dynamics of external environmental and internal patho/physiological stimuli, which activate regulatory systems including the hypothalamic-pituitary-adrenal axis and autonomic nervous system. Together with other systems, they enable feedback interactions between all of the person's system domains and impact on his system's entropy. These interactions affect individual behaviors, emotional, and cognitive responses, as well as molecular, cellular, and organ system level functions. This paper explores the hypothesis that health is an emergent state that arises from hierarchical network interactions between a person's external environment and internal physiology. As a result, the concept of health synthesizes available qualitative and quantitative evidence of interdependencies and constraints that indicate its top-down and bottom-up causative mechanisms. Thus, to provide effective care, we must use strategies that combine person-centeredness with the scientific approaches that address the molecular network physiology, which together underpin health and disease. Moreover, we propose that good health can also be promoted by strengthening resilience and self-efficacy at the personal and social level, and via cohesion at the population level. Understanding health as a state that is both individualized and that emerges from multi-scale interdependencies between microlevel physiological mechanisms of health and disease and macrolevel societal domains may provide the basis for a new public discourse for health service and health system redesign

Examining sex differences in pleiotropic effects for depression and smoking using polygenic and gene‐region aggregation techniques

Sex differences in rates of depression are thought to contribute to sex differences in smoking initiation (SI) and number of cigarettes smoked per day (CPD). One hypothesis is that women smoke as a strategy to cope with anxiety and depression, and have difficulty quitting because of concomitant changes in hypothalamic–pituitary–adrenocortical (HPA) axis function during nicotine withdrawal states. Despite evidence of biological ties, research has not examined whether genetic factors that contribute to depression‐smoking comorbidity differ by sex. We utilized two statistical aggregation techniques—polygenic scores (PGSs) and sequence kernel association testing—to assess the degree of pleiotropy between these behaviors and moderation by sex in the Health and Retirement Study (N = 8,086). At the genome‐wide level, we observed associations between PGSs for depressive symptoms and SI, and measured SI and depressive symptoms (all p < .01). At the gene level, we found evidence of pleiotropy in FKBP5 for SI (p = .028), and sex‐specific pleiotropy in females in NR3C2 (p = .030) and CHRNA5 (p = .025) for SI and CPD, respectively. Results suggest bidirectional associations between depression and smoking may be partially accounted for by shared genetic factors, and genetic variation in genes related to HPA‐axis functioning and nicotine dependence may contribute to sex differences in SI and CPD.Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/150605/1/ajmgb32748.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/150605/2/ajmgb32748_am.pd