Search results for "Uniqueness"
showing 10 items of 211 documents
Localization and separation of solutions for Fredholm integral equations
2020
[EN] In this paper, we establish a qualitative study of nonlinear Fredholm integral equations, where we will carry out a study on the localization and separation of solutions. Moreover, we consider an efficient algorithm to approximate a solution. To do this, we study the semilocal convergence of an efficient third order iterative scheme for solving nonlinear Fredholm integral equations under mild conditions. The novelty of our work lies in the fact that this study involves first order Frechet derivative and mild conditions. A numerical example involving nonlinear Fredholm integral equations, is solved to show the domains of existence and uniqueness of solutions. The applicability of the it…
Risignificare l’autonomia nell’età contemporanea: spunti di riflessione dalla pedagogia di Romano Guardini
2022
Tra i principi fondanti la vita dell’uomo contemporaneo, come imperante emerge l’autonomia. Nata nella modernità come valorizzazione della soggettività, l’autonomia ha poi assunto un indefinito carattere di assolutizzazione, tendente a denaturare l’essenza più profonda dell’essere personale. Il presente scritto si propone di accogliere l’analisi che dell’autonomia – e della persona - propone il pensatore Romano Guardini, e da essa lasciar emergere i tratti costitutivi, nel tentativo di assumerli come direzioni di senso preziose per una attuale e necessaria risignificazione pedagogica dell’autonomia: un’autonomia rispettosa dell’essenza della persona, quindi capace di porsi in dialogo con l’…
Erratum: An Inverse Backscatter Problem for Electric Impedance Tomography
2011
We fix an incorrect statement from our paper [M. Hanke, N. Hyvonen, and S. Reusswig, SIAM J. Math. Anal., 41 (2009), pp. 1948–1966] claiming that two different perfectly conducting inclusions necessarily have different backscatter in impedance tomography. We also present a counterexample to show that this kind of nonuniqueness does indeed occur.
An inverse problem for the fractional Schrödinger equation in a magnetic field
2020
This paper shows global uniqueness in an inverse problem for a fractional magnetic Schrodinger equation (FMSE): an unknown electromagnetic field in a bounded domain is uniquely determined up to a natural gauge by infinitely many measurements of solutions taken in arbitrary open subsets of the exterior. The proof is based on Alessandrini's identity and the Runge approximation property, thus generalizing some previous works on the fractional Laplacian. Moreover, we show with a simple model that the FMSE relates to a long jump random walk with weights.
A RADIATION CONDITION FOR UNIQUENESS IN A WAVE PROPAGATION PROBLEM FOR 2-D OPEN WAVEGUIDES
2009
We study the uniqueness of solutions of Helmholtz equation for a problem that concerns wave propagation in waveguides. The classical radiation condition does not apply to our problem because the inhomogeneity of the index of refraction extends to infinity in one direction. Also, because of the presence of a waveguide, some waves propagate in one direction with different propagation constants and without decaying in amplitude. Our main result provides an explicit condition for uniqueness which takes into account the physically significant components, corresponding to guided and non-guided waves; this condition reduces to the classical Sommerfeld-Rellich condition in the relevant cases. Final…
Isotropic p-harmonic systems in 2D Jacobian estimates and univalent solutions
2016
The core result of this paper is an inequality (rather tricky) for the Jacobian determinant of solutions of nonlinear elliptic systems in the plane. The model case is the isotropic (rotationally invariant) p-harmonic system ...
Multiplicity, Overtaking and Convergence in the Lucas Two-Sector Growth Model
2002
This paper provides the complete closed-form solution to the Lucas two-sector model of endogenous growth. We study the issues of existence, unique-ness, multiplicity, positivity, transitional dynamics and long-run growth, re-lated to the competitive equilibrium paths. We identify the parameter range where the different results hold and deduce the entire trajectories for the original variables. We revise the results on convergence and overtaking which arise from this model, and prove that the parameterization currently used as the background for an explanation of economic miracles and disasters, is not satisfactory because of its counterintuitive implications.
Large solutions for nonlinear parabolic equations without absorption terms
2012
In this paper we give a suitable notion of entropy solution of parabolic $p-$laplacian type equations with $1\leq p<2$ which blows up at the boundary of the domain. We prove existence and uniqueness of this type of solutions when the initial data is locally integrable (for $1<p<2$) or integrable (for $p=1$; i.e the Total Variation Flow case).
A Fisher–Kolmogorov equation with finite speed of propagation
2010
Abstract In this paper we study a Fisher–Kolmogorov type equation with a flux limited diffusion term and we prove the existence and uniqueness of finite speed moving fronts and the existence of some explicit solutions in a particular regime of the equation.
Existence and uniqueness of solution to several kinds of differential equations using the coincidence theory
2015
The purpose of this article is to study the existence of a coincidence point for two mappings defined on a nonempty set and taking values on a Banach space using the fixed point theory for nonexpansive mappings. Moreover, this type of results will be applied to obtain the existence of solutions for some classes of ordinary differential equations. Ministerio de Economía y Competitividad Junta de Andalucía