Search results for "Nonlinear"

Multiple solutions for (p,2)-equations at resonance

2019

We consider a nonlinear nonhomogeneous Dirichlet problem driven by the sum of a p-Laplacian and a Laplacian and a reaction term which is (p− 1)-linear near ±∞ and resonant with respect to any nonprincipal variational eigenvalue of (−∆p, W01,p(Ω)). Using variational tools together with truncation and comparison techniques and Morse Theory (critical groups), we establish the existence of six nontrivial smooth solutions. For five of them we provide sign information and order them.

Modeling multiple taxis: Tumor invasion with phenotypic heterogeneity, haptotaxis, and unilateral interspecies repellence

2021

We provide a short review of existing models with multiple taxis performed by (at least) one species and consider a new mathematical model for tumor invasion featuring two mutually exclusive cell phenotypes (migrating and proliferating). The migrating cells perform nonlinear diffusion and two types of taxis in response to non-diffusing cues: away from proliferating cells and up the gradient of surrounding tissue. Transitions between the two cell subpopulations are influenced by subcellular (receptor binding) dynamics, thus conferring the setting a multiscale character. We prove global existence of weak solutions to a simplified model version and perform numerical simulations for the full se…

Critical Phenomena and Diffusion in Complex Systems

2008

The predictive power of power-laws: An empirical time-arrow based investigation

2022

The efficient market hypothesis forbids any predictability towards future, but there is no such restriction in the case of reversed-looking approaches. We analyze if this asymmetry in non-predictability is reflected in the statistical features of financial time series. Our study is based on the analysis of the length-distribution of periods with high variability, and introduces time-asymmetric modifications of the method which are capable of revealing differences of the time series in forward and reversed time. We show that the future and reversed-looking time-series possess very similar properties, with some features being distinguishable with our method. Our findings give also evidence of…

Seismic Behavior of Lisbon Mixed Masonry-RC Buildings With Historical Value: A Contribution for the Practical Assessment

2018

The fact that linear analysis is still the most used procedure in the design engineering offices, studies which addresses issues associated to the estimation of the structural behavior factor values are relevant. In this study, the behavior factor of a particular type of mixed masonry-reinforced concrete buildings in Lisbon is estimated. The typology chosen in this study represents 30% of building stock in Lisbon; these buildings were built between 1930 and 1960 and thus were designed without considering the seismic-design requirements proposed in current codes. The evaluation of the behavior factors was based on the use of nonlinear static analyses, performed in the form of the sensitivity…

A bounded version of bosonic creation and annihilation operators and their related quasi-coherent states

2007

Coherent states are usually defined as eigenstates of an unbounded operator, the so-called annihilation operator. We propose here possible constructions of {\em quasi-coherent states}, which turn out to be {\em quasi} eigenstate of a \underline{bounded} operator related to an annihilation-like operator. We use this bounded operator to construct a sort of modified harmonic oscillator and we analyze the dynamics of this oscillator from an algebraic point of view.

Decay estimates in the supremum norm for the solutions to a nonlinear evolution equation

2014

We study the asymptotic behaviour, as t → ∞, of the solutions to the nonlinear evolution equationwhere ΔpNu = Δu + (p−2) (D2u(Du/∣Du∣)) · (Du/∣Du∣) is the normalized p-Laplace equation and p ≥ 2. We show that if u(x,t) is a viscosity solution to the above equation in a cylinder Ω × (0, ∞) with time-independent lateral boundary values, then it converges to the unique stationary solution h as t → ∞. Moreover, we provide an estimate for the decay rate of maxx∈Ω∣u(x,t) − h(x)∣.

Ultrarelativistic bound states in the spherical well

2016

We address an eigenvalue problem for the ultrarelativistic (Cauchy) operator $(-\Delta )^{1/2}$, whose action is restricted to functions that vanish beyond the interior of a unit sphere in three spatial dimensions. We provide high accuracy spectral datafor lowest eigenvalues and eigenfunctions of this infinite spherical well problem. Our focus is on radial and orbital shapes of eigenfunctions. The spectrum consists of an ordered set of strictly positive eigenvalues which naturally splits into non-overlapping, orbitally labelled $E_{(k,l)}$ series. For each orbital label $l=0,1,2,...$ the label $k =1,2,...$ enumerates consecutive $l$-th series eigenvalues. Each of them is $2l+1$-degenerate. …

Some Non-linear Geometrical Properties of Banach Spaces

2014

In this survey we report on very recent results about some non-linear geometrical properties of many classes of real and complex Banach spaces and uniform algebras, including the ball algebra \(\fancyscript{A}_u(B_X)\) of all uniformly continuous functions on the closed unit ball and holomorphic on the open unit ball of a complex Banach space \(X\). These geometrical properties are: Polynomial numerical index, Polynomial Daugavet property and Bishop-Phelp-Bollobas property for multilinear mappings.

An extension of Guo's theorem via k--contractive retractions

2006

Abstract Let X be a infinite-dimensional Banach space. We generalize Guo's Theorem [D.J. Guo, Eigenvalues and eigenvectors of nonlinear operators, Chinese Ann. Math. 2 (1981) 65–80 [English]] to k- ψ -contractions and condensing mappings, under a condition which depends on the infimum k ψ of all k ⩾ 1 for which there exists a k- ψ -contractive retraction of the closed unit ball of the space X onto its boundary.