Advanced Search

Si considera il problema al contorno $-\mathrm{\Delta }u=f(x,u)+ϵ\psi (x,u)$ in $\mathrm{\Omega }$, $u|\partial \mathrm{\Omega }=0$, dove $\mathrm{\Omega }\in {ℝ}^n$ è un aperto limitato e connesso ed $ϵ$ è un parametro reale. Si prova che, se $f(x,s)+ϵ\psi (x,s)$ è «superlineare» ed $ϵ$ è abbastanza piccolo, il problema precedente ha almeno tre soluzioni distinte.

Si considera il problema al contorno $-\mathrm{\Delta }u=f(x,u)+ϵ\psi (x,u)$ in $\mathrm{\Omega }$, $u|\partial \mathrm{\Omega }=0$, dove $\mathrm{\Omega }\in {ℝ}^n$ è un aperto limitato e connesso ed $ϵ$ è un parametro reale. Si prova che, se $f(x,s)+ϵ\psi (x,s)$ è «superlineare» ed $ϵ$ è abbastanza piccolo, il problema precedente ha almeno tre soluzioni distinte.

We study properties of variational measures associated with certain conditionally convergent integrals in ${ℝ}^m$. In particular we give a full descriptive characterization of these integrals.

Some relationships between the vector valued Henstock and McShane integrals are investigated. An integral for vector valued functions, defined by means of partitions of the unity (the PU-integral) is studied. In particular it is shown that a vector valued function is McShane integrable if and only if it is both Pettis and PU-integrable. Convergence theorems for the Henstock variational and the PU integrals are stated. The families of multipliers for the Henstock and the Henstock variational integrals...

Some properties of absolutely continuous variational measures associated with local systems of sets are established. The classes of functions generating such measures are described. It is shown by constructing an example that there exists a $𝒫$-adic path system that defines a differentiation basis which does not possess Ward property.

We present a Cauchy test for the almost derivability of additive functions of bounded BV sets. The test yields a full descriptive definition of a coordinate free Riemann type integral.

We study the integrability of Banach space valued strongly measurable functions defined on $[0,1]$. In the case of functions $f$ given by ${\sum }_{n=1}^{\infty }{x}_n{\chi }_{E_n}$, where $x_n$ are points of a Banach space and the sets $E_n$ are Lebesgue measurable and pairwise disjoint subsets of $[0,1]$, there are well known characterizations for Bochner and Pettis integrability of $f$. The function $f$ is Bochner integrable if and only if the series ${\sum }_{n=1}^{\infty }{x}_n\left|E_n\right|$ is absolutely convergent. Unconditional convergence of the series is equivalent to Pettis integrability of $f$....

We study the integrability of Banach valued strongly measurable functions defined on $[0,1]$. In case of functions $f$ given by ${\sum }_{n=1}^{\infty }{x}_n{\chi }_{E_n}$, where $x_n$ belong to a Banach space and the sets $E_n$ are Lebesgue measurable and pairwise disjoint subsets of $[0,1]$, there are well known characterizations for the Bochner and for the Pettis integrability of $f$ (cf Musial (1991)). In this paper we give some conditions for the Kurzweil-Henstock and the Kurzweil-Henstock-Pettis integrability of such functions.