Si studiano le applicazioni $p$-tangenti da ${\mathbb{R}}^m$ a ${\mathbb{S}}^n$ date come estensioni omogenee di $k$-forme armoniche. Vengono ricavate condizioni necessarie sul grado $k$ affinche tali applicazioni $p$-tangenti siano di energia minima. Una classificazione completa viene data nel caso in cui tali applicazioni tangenti di energia minima vadano da ${\mathbb{R}}^8$ su ${\mathbb{S}}^4$.

Given a metric space $X$ we consider a general class of functionals which measure the cost of a path in $X$ joining two given points $x_0$ and $x_1$, providing abstract existence results for optimal paths. The results are then applied to the case when $X$ is aWasserstein space of probabilities on a given set $\Omega$ and the cost of a path depends on the value of classical functionals over measures. Conditions for linking arbitrary extremal measures ${\mu }_0$ and ${\mu }_1$ by means of finite cost paths are given.

We study the existence of spatial periodic solutions for nonlinear elliptic equations $-\Delta u+g(x,u\left(x\right))=0,x\in {ℝ}^N$ where $g$ is a continuous function, nondecreasing w.r.t. $u$. We give necessary and sufficient conditions for the existence of periodic solutions. Some cases with nonincreasing functions $g$ are investigated as well. As an application we analyze the mathematical model of electron beam focusing system and we prove the existence of positive periodic solutions for the envelope equation. We present also numerical simulations....

We study the existence of spatial periodic solutions for nonlinear elliptic equations $-\Delta u+g(x,u\left(x\right))=0,x\in {ℝ}^N$ where g is a continuous function, nondecreasing w.r.t. u. We give necessary and sufficient conditions for the existence of periodic solutions. Some cases with nonincreasing functions g are investigated as well. As an application we analyze the mathematical model of electron beam focusing system and we prove the existence of positive periodic solutions for the envelope equation. We present also numerical simulations. ...

By using the least action principle and minimax methods in critical point theory, some existence theorems for periodic solutions of second order Hamiltonian systems are obtained.

Two theorems about the existence of periodic solutions with prescribed energy for second order Hamiltonian systems are obtained. One gives existence for almost all energies under very natural conditions. The other yields existence for all energies under a further condition.

In this paper, by using the least action principle, Sobolev's inequality and Wirtinger's inequality, some existence theorems are obtained for periodic solutions of second-order Hamiltonian systems with a p-Laplacian under subconvex condition, sublinear growth condition and linear growth condition. Our results generalize and improve those in the literature.

In this paper, we deal with the existence of periodic solutions of the $p\left(t\right)$-Laplacian Hamiltonian system $$\left\{\begin{array}{c}{\displaystyle \frac{\mathrm{d}}{\mathrm{d}t}}\left(\right|\dot{u}\left(t\right){|}^{p\left(t\right)-2}\dot{u}\left(t\right))=\nabla F(t,u\left(t\right))\text{a.e.}t\in [0,T],\hfill \\ u\left(0\right)-u\left(T\right)=\dot{u}\left(0\right)-\dot{u}\left(T\right)=0.\hfill \end{array}\right.$$ Some new existence theorems are obtained by using the least action principle and minimax methods in critical point theory, and our results generalize and improve some existence theorems.