This paper is concerned with the global asymptotic stability of the zero solution of the half-linear differential system $$x^{\text{'}}=-e\left(t\right)x+f\left(t\right){\phi }_{p^{*}}\left(y\right),y^{\text{'}}=-g\left(t\right){\phi }_p\left(x\right)-h\left(t\right)y,$$ where $p>1$, $p^{*}>1$ ($1/p+1/p^{*}=1$), and ${\phi }_q\left(z\right)={\left|z\right|}^{q-2}z$ for $q=p$ or $q=p^{*}$. The coefficients are not assumed to be positive. This system includes the linear differential system ${𝐱}^{\text{'}}=A\left(t\right)𝐱$ with $A\left(t\right)$ being a $2\times 2$ matrix as a special case. Our results are new even in the linear case ($p=p^{*}=2$). Our results also answer the question whether the zero solution of the linear system is asymptotically stable even when Coppel’s condition does not hold...

We consider a simple model for the immune system in which virus are able to undergo mutations and are in competition with leukocytes. These mutations are related to several other concepts which have been proposed in the literature like those of shape or of virulence – a continuous notion. For a given species, the system admits a globally attractive critical point. We prove that mutations do not affect this picture for small perturbations and under strong structural assumptions. Based on numerical...

We consider a simple model for the immune system in which virus are able to undergo mutations and are in competition with leukocytes. These mutations are related to several other concepts which have been proposed in the literature like those of shape or of virulence – a continuous notion. For a given species, the system admits a globally attractive critical point. We prove that mutations do not affect this picture for small perturbations and under strong structural assumptions. Based on numerical...