For general matrix summability methods, we find necessary and sufficient conditions for such methods to be stronger than multisummability. In a second part we show the existence of power series which are not multisummable but can be summed by a matrix method satisfying the conditions mentioned above

Si studia l'omogeneizzazione periodica di una particolare equazione differenziale ordinaria. Si studiano alcune proprietà dell'equazione omogeneizzata e in certi casi se ne trova la formula esplicita.

Solutions to singular linear ordinary differential equations with analytic coefficients are found in the form of Laplace type integrals.

Theory of chemical reactions in complex mixtures exhibits the following problem. Single reacting species follow an intrinsic kinetic law. However, the observable quantity, which is a mean of individual concentrations, follows a different law. This one is called «alias» of intrinsic kinetics. In this paper the phenomenon of alias of uniform families of differential equations is discussed in general terms.

The paper describes the general form of an ordinary differential equation of the second order which allows a nontrivial global transformation consisting of the change of the independent variable and of a nonvanishing factor. A result given by J. Aczél is generalized. A functional equation of the form $$f(t,vy,wy+uvz)=f(x,y,z)u^{2}v+g(t,x,u,v,w)vz+h(t,x,u,v,w)y+2uwz$$ is solved on $ℝ$ for $y\ne 0$, $v\ne 0.$

Perceptions about function changes are represented by rules like “If X is SMALL then Y is QUICKLY INCREASING.” The consequent part of a rule describes a granule of directions of the function change when X is increasing on the fuzzy interval given in the antecedent part of the rule. Each rule defines a granular differential and a rule base defines a granular derivative. A reconstruction of a fuzzy function given by the granular derivative and the initial value given by the rule is similar to Euler’s...

This paper is concerned with square integrable quasi-derivatives for any solution of a general quasi-differential equation of $n$th order with complex coefficients $M\left[y\right]-\lambda wy=wf(t,y^{\left[0\right]},...,y^{[n-1]})$, $t\in [a,b)$ provided that all $r$th quasi-derivatives of solutions of $M\left[y\right]-\lambda wy=0$ and all solutions of its normal adjoint $M^{+}\left[z\right]-\overline{\lambda }wz=0$ are in $L_w^2(a,b)$ and under suitable conditions on the function $f$.

The paper deals with the oscillation of a differential equation $L_{4}y+P\left(t\right)L_{2}y+Q\left(t\right)y\equiv 0$ as well as with the structure of its fundamental system of solutions.

The zeros $c_k\left(\nu \right)$ of the solution $z(t,\nu )$ of the differential equation $z^{\text{'}\text{'}}+q(t,\nu )z=0$ are investigated when $\underset{t\to \infty }{lim}q(t,\nu )=1$, ${\int }^{\infty }|q(t,\nu )-1|dt<\infty$ and $q(t,\nu )$ has some monotonicity properties as $t\to \infty$. The notion $c_{\kappa }\left(\nu \right)$ is introduced also for $\kappa$ real, too. We are particularly interested in solutions $z(t,\nu )$ which are “close" to the functions $sint$, $cost$ when $t$ is large. We derive a formula for $d{c}_{\kappa }\left(\nu \right)/d\nu$ and apply the result to Bessel differential equation, where we introduce new pair of linearly independent solutions replacing the usual pair $J_{\nu }\left(t\right)$, $Y_{\nu }\left(t\right)$. We show the concavity of $c_{\kappa }\left(\nu \right)$ for $\left|\nu \right|\ge \frac{1}{2}$ and also...