Positive solutions of the nonlinear second-order differential equation $\left(p\left(t\right)\right|x^{\text{'}}{|}^{\alpha -1}{x}^{\text{'}}{)}^{\text{'}}+q\left(t\right){\left|x\right|}^{\beta -1}x=0,\alpha >\beta >0,$ are studied under the assumption that p, q are generalized regularly varying functions. An application of the theory of regular variation gives the possibility of obtaining necessary and sufficient conditions for existence of three possible types of intermediate solutions, together with the precise information about asymptotic behavior at infinity of all solutions belonging to each type of solution classes.

We propose and analyze a mathematical model of hematopoietic stem cell dynamics. This model takes into account a finite number of stages in blood production, characterized by cell maturity levels, which enhance the difference, in the hematopoiesis process, between dividing cells that differentiate (by going to the next stage) and dividing cells that keep the same maturity level (by staying in the same stage). It is described by a system of n nonlinear differential equations with n delays. We study...

In this paper we prove two results. The first is an extension of the result of G. D. Jones [4]: (A) Every nontrivial solution for $$\left\}\begin{array}{c}{(-1)}^n{u}^{\left(2n\right)}+f(t,u)=0,\text{in}(\alpha ,\infty ),u^{\left(i\right)}\left(\xi \right)=0,i=0,1,\cdots ,n-1,\text{and}\xi \in (\alpha ,\infty ),\hfill \end{array}\right.$$ must be unbounded, provided $f(t,z)z\ge 0$, in $E\times ℝ$ and for every bounded subset $I$, $f(t,z)$ is bounded in $E\times I$. (B) Every bounded solution for ${(-1)}^n{u}^{\left(2n\right)}+f(t,u)=0$, in $ℝ$, must be constant, provided $f(t,z)z\ge 0$ in $ℝ\times ℝ$ and for every bounded subset $I$, $f(t,z)$ is bounded in $ℝ\times I$.

We give an equivalence criterion on property A and property B for delay third order linear differential equations. We also give comparison results on properties A and B between linear and nonlinear equations, whereby we only suppose that nonlinearity has superlinear growth near infinity.

The asymptotic behaviour for $t\to \infty$ of the solutions to a one-dimensional model for thermo-visco-plastic behaviour is investigated in this paper. The model consists of a coupled system of nonlinear partial differential equations, representing the equation of motion, the balance of the internal energy, and a phase evolution equation, determining the evolution of a phase variable. The phase evolution equation can be used to deal with relaxation processes. Rate-independent hysteresis effects in the strain-stress...

In the paper the fourth order nonlinear differential equation $y^{\left(4\right)}+{\left(q\left(t\right)y^{\text{'}}\right)}^{\text{'}}+r\left(t\right)f\left(y\right)=0$, where $q\in C^1\left([0,\infty )\right)$, $r\in C^0\left([0,\infty )\right)$, $f\in C^0\left(R\right)$, $r\ge 0$ and $f\left(x\right)x>0$ for $x\ne 0$ is considered. We investigate the asymptotic behaviour of nonoscillatory solutions and give sufficient conditions under which all nonoscillatory solutions either are unbounded or tend to zero for $t\to \infty$.