It is considered the mathematical model of a benchmark hydroelectric power plant containing a water reservoir (lake), two water conduits (the tunnel and the turbine penstock), the surge tank and the hydraulic turbine; all distributed (Darcy-Weisbach) and local hydraulic losses are neglected,the only energy dissipator remains the throttling of the surge tank. Exponential stability would require asymptotic stability of the difference operator associated to the model. However in this case this stability...

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 the setting of a real Hilbert space $\mathscr{H}$, we investigate the asymptotic behavior, as time t goes to infinity, of trajectories of second-order evolution equations            ü(t) + γ$\dot{u}$(t) + ∇ϕ(u(t)) + A(u(t)) = 0, where ∇ϕ is the gradient operator of a convex differentiable potential function ϕ: $\mathscr{H}\to ℝ$,A: $\mathscr{H}\to \mathscr{H}$ is a maximal monotone operator which is assumed to beλ-cocoercive, and γ > 0 is a damping parameter. Potential and non-potential effects are associated respectively to ∇ϕ and A. Under condition...

In the setting of a real Hilbert space $\mathscr{H}$, we investigate the asymptotic behavior, as time t goes to infinity, of trajectories of second-order evolution equations            ü(t) + γ$\dot{u}$(t) + ∇ϕ(u(t)) + A(u(t)) = 0, where ∇ϕ is the gradient operator of a convex differentiable potential function ϕ : $\mathscr{H}\to ℝ$, A : $\mathscr{H}\to \mathscr{H}$ is a maximal monotone operator which is assumed to be λ-cocoercive, and γ > 0 is a damping parameter. Potential and non-potential effects are associated respectively to ∇ϕ and A. Under condition...

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 $ℝ\times I$.

Asymptotic behaviour of oscillatory solutions of the fourth-order nonlinear differential equation with quasiderivates $y^{\left[4\right]}+r\left(t\right)f\left(y\right)=0$ is studied.