Search results for " Matematica"

Nonlinear concave-convex problems with indefinite weight

2021

We consider a parametric nonlinear Robin problem driven by the p-Laplacian and with a reaction having the competing effects of two terms. One is a parametric (Formula presented.) -sublinear term (concave nonlinearity) and the other is a (Formula presented.) -superlinear term (convex nonlinearity). We assume that the weight of the concave term is indefinite (that is, sign-changing). Using the Nehari method, we show that for all small values of the parameter (Formula presented.), the problem has at least two positive solutions and also we provide information about their regularity.

A short note on O*-algebras and quantum dynamics

2009

We review some recent results concerning algebraic dynamics and O*-algebras. We also give a perturbative condition which can be used, in connection with previous results, to define a time evolution via a limiting procedure.

A survey on solvable sesquilinear forms

2018

The aim of this paper is to present a unified theory of many Kato type representation theorems in terms of solvable forms on a Hilbert space \((H,\langle\cdot,\cdot\rangle)\) In particular, for some sesquilinear forms Ω on a dense domain \(D\subseteq\mathcal {H}\) one looks for a representation \(\Omega(\xi,\eta)= \langle T\xi,\eta\rangle\) \((\xi\epsilon\mathcal{D}\mathcal(T),\eta\epsilon D)\) where T is a densely defined closed operator with domain \(D(\mathcal{T})\subseteq \mathcal{D}\). There are two characteristic aspects of a solvable form on H. One is that the domain of the form can be turned into a reexive Banach space that need not be a Hilbert space. The second one is that represe…

MR3667002 Reviewed Vogt, Dietmar(D-BUW) Hadamard operators on D′(Ω). (English summary) Math. Nachr. 290 (2017), no. 8-9, 1374–1380. 46F10 (46F12 47B3…

2017

In this paper, the Hadamard operators, i.e. a particular class of continuous linear operators on D′(Ω) whose set of eigenvectors is the class of monomials, are considered on an open set Ω⊂Rd. Specifically, Hadamard operators L are characterized by the multiplicative convolution, that is, there exists a distribution T such that L(S)=S⋆T, where the multiplicative convolution ⋆ is defined by (S⋆T)ϕ=Sy(Txϕ(xy)). To obtain this characterization, the author defines a particular extension to D(Ω˜), where Ω˜:=⋃a∈RdaΩ, of the transpose of Hadamard operators. This result is a generalization of a previous work of the author where only the case Ω=Rd was considered.

On the solutions of the differential overland flow equation

2010

In this paper we study the overland flow equation for an arbitrary positive value of the rating exponent m. We write the general solution of the equation and generalize the series solution given in [1] and [2]. Finally, we show how the five solutions presented in [5] are actually a special case of a general formula valid for any rational m≥1.

Painlev\'{e} analysis for a generalized nonlinear Schr\"{o}dinger equation

2008

On universality of critical behavior in the focusing nonlinear Schrödinger equation, elliptic umbilic catastrophe and the Tritronquée solution to the…

2008

We argue that the critical behavior near the point of “gradient catastrophe” of the solution to the Cauchy problem for the focusing nonlinear Schrodinger equation \(i\epsilon \varPsi _{t}+\frac{\epsilon^{2}}{2}\varPsi _{xx}+|\varPsi |^{2}\varPsi =0\) , e ≪1, with analytic initial data of the form \(\varPsi (x,0;\epsilon)=A(x)e^{\frac{i}{\epsilon}S(x)}\) is approximately described by a particular solution to the Painleve-I equation.

C*-seminorms generated by families of biweights on partial *-algebras

2011

If A[t] is a topological partial *-algebra with unit, topologized by the family of seminorms {p_a}, the notion of bounded element is defined, and some conditions to obtain an unbounded C*-seminorm q(x)=sup p_a(x) on A[t] with domain the subalgebra of bounded elements of A[t] are given.

Formation of Coherent Structures in Kolmogorov Flow with Stratification and Drag

2014

We study a weakly stratified Kolmogorov flow under the effect of a small linear drag. We perform a linear stability analysis of the basic state. We construct the finite dimensional dynamical system deriving from the truncated Fourier mode approximation. Using the Reynolds number as bifurcation parameter we build the corresponding diagram up to Re=100. We observe the coexistence of three coherent structures.

On the Prandtl Boundary Layer Equations in Presence of Corner Singularities

2014

In this paper we prove the well-posedness of the Prandtl boundary layer equations on a periodic strip when the initial and the boundary data are not assigned to be compatible.