scholarly journals A Uniqueness Result for a Simple Superlinear Eigenvalue Problem

2021 ◽  
Vol 31 (2) ◽  
Author(s):  
Michael Herrmann ◽  
Karsten Matthies
Keyword(s):  
Eigenvalue Problem ◽  
Numerical Simulations ◽  
Convolution Operator ◽  
Existence And Uniqueness ◽  
Uniqueness Result ◽  
Constitutive Laws ◽  
Parameter Family ◽  
Shape Constraint ◽  
Special Case ◽  
Nonlinear Eigenfunctions

AbstractWe study the eigenvalue problem for a superlinear convolution operator in the special case of bilinear constitutive laws and establish the existence and uniqueness of a one-parameter family of nonlinear eigenfunctions under a topological shape constraint. Our proof uses a nonlinear change of scalar parameters and applies Krein–Rutman arguments to a linear substitute problem. We also present numerical simulations and discuss the asymptotics of two limiting cases.

The eigenvalue problem for Hessian type operator

2021 ◽  
Author(s):  
Xinqun Mei
Keyword(s):  
Eigenvalue Problem ◽  
Existence And Uniqueness ◽  
Dirichlet Boundary ◽  
Type Equation ◽  
Uniqueness Result ◽  
Type Operator

In this paper, we establish a global [Formula: see text] estimates for a Hessian type equation with homogeneous Dirichlet boundary. By the method of sub and sup solution, we get an existence and uniqueness result for the eigenvalue problem of a Hessian type operator.

Existence and uniqueness results for a class of elliptic equations with exponential nonlinearity

2005 ◽  
Vol 135 (5) ◽  
pp. 959-983
Author(s):  
Kwangseok Choe
Keyword(s):  
Eigenvalue Problem ◽  
Elliptic Equations ◽  
Existence And Uniqueness ◽  
Uniqueness Result ◽  
Existence Results ◽  
Implicit Function ◽  
Exponential Nonlinearity ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Semilinear Elliptic

We establish existence results for a class of semilinear elliptic equations with exponential nonlinearity by studying a suitable eigenvalue problem. We also establish a uniqueness result for those equations by making use of the implicit function theorem.

Existence and uniqueness results for a class of elliptic equations with exponential nonlinearity

2005 ◽  
Vol 135 (5) ◽  
pp. 959-983 ◽  
Author(s):  
Kwangseok Choe
Keyword(s):  
Eigenvalue Problem ◽  
Elliptic Equations ◽  
Existence And Uniqueness ◽  
Uniqueness Result ◽  
Existence Results ◽  
Implicit Function ◽  
Exponential Nonlinearity ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Semilinear Elliptic

We establish existence results for a class of semilinear elliptic equations with exponential nonlinearity by studying a suitable eigenvalue problem. We also establish a uniqueness result for those equations by making use of the implicit function theorem.

DISSIPATIVE BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS IN INFINITE DIMENSIONS

2006 ◽  
Vol 09 (01) ◽  
pp. 155-168 ◽  
Author(s):  
FULVIA CONFORTOLA
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Hilbert Spaces ◽  
Stochastic Partial Differential Equations ◽  
Existence And Uniqueness ◽  
Backward Stochastic Differential Equations ◽  
Uniqueness Result ◽  
Infinite Dimensions ◽  
Partial Differential

We prove an existence and uniqueness result for a class of backward stochastic differential equations (BSDE) with dissipative drift in Hilbert spaces. We also give examples of stochastic partial differential equations which can be solved with our result.

scholarly journals On the Bean critical-state model in superconductivity

1996 ◽  
Vol 7 (3) ◽  
pp. 237-247 ◽  
Author(s):  
L. Prigozhin
Keyword(s):  
Variational Inequalities ◽  
Critical State ◽  
Existence And Uniqueness ◽  
Critical State Model ◽  
Type Ii ◽  
Two Dimensional ◽  
Axially Symmetric ◽  
Uniqueness Of The Solution ◽  
Type Ii Superconductivity ◽  
Special Case

We consider two-dimensional and axially symmetric critical-state problems in type-II superconductivity, and show that these problems are equivalent to evolutionary quasi-variational inequalities. In a special case, where the inequalities become variational, the existence and uniqueness of the solution are proved.

A Combinatorial Distinction Between Unit Circles and Straight Lines: How Many Coincidences Can they Have?

2009 ◽  
Vol 18 (5) ◽  
pp. 691-705 ◽  
Author(s):  
GYÖRGY ELEKES ◽  
MIKLÓS SIMONOVITS ◽  
ENDRE SZABÓ
Keyword(s):  
Parameter Family ◽  
Sufficient Condition ◽  
Simple Application ◽  
Quadratic Number ◽  
General Sufficient Condition ◽  
Family Of Curves ◽  
Unit Circles ◽  
Triple Points ◽  
Straight Lines ◽  
Special Case

We give a very general sufficient condition for a one-parameter family of curves not to have n members with ‘too many’ (i.e., a near-quadratic number of) triple points of intersections. As a special case, a combinatorial distinction between straight lines and unit circles will be shown. (Actually, this is more than just a simple application; originally this motivated our results.)

THE ROLE OF OXYGEN IN TISSUE MAINTENANCE: MATHEMATICAL MODELING AND QUALITATIVE ANALYSIS

2008 ◽  
Vol 18 (08) ◽  
pp. 1409-1441 ◽  
Author(s):  
AVNER FRIEDMAN ◽  
BEI HU
Keyword(s):  
Mathematical Modeling ◽  
Free Boundary ◽  
Qualitative Analysis ◽  
Phase I ◽  
Stationary Solution ◽  
Oxygen Concentration ◽  
Existence And Uniqueness ◽  
Symmetric Case ◽  
Special Case

The cells in a tissue occupying a region Ωt are divided according to their cycling phase. The density pi of cells in phase i depends on the spatial variable x, the time t, and the time si since the cells entered in phase i. The pi(x, t, si) and the oxygen concentration w(x, t) satisfy a system of PDEs in Ωt, and the boundary of Ωt is a free boundary. We denote by [Formula: see text] the oxygen concentration on the free boundary and consider the radially symmetric case, so that Ωt = {r < R(t)}. We prove that R(t) is always bounded; furthermore, if [Formula: see text] is small, then R(t) → 0 as t → ∞, and if [Formula: see text] is large, then R(t) ≥ c > 0 for all t. Finally, we prove the existence and uniqueness of a stationary solution in a special case.

scholarly journals General fractional financial models of awareness with Caputo–Fabrizio derivative

2020 ◽  
Vol 12 (11) ◽  
pp. 168781402097552
Author(s):  
Amr MS Mahdy ◽  
Yasser Abd Elaziz Amer ◽  
Mohamed S Mohamed ◽  
Eslam Sobhy
Keyword(s):  
Mathematical Model ◽  
Fixed Point ◽  
Numerical Simulations ◽  
Caputo Derivative ◽  
Existence And Uniqueness ◽  
Financial Models ◽  
Whole Number ◽  
Fractional System ◽  
Set Up ◽  
Theoretical Results

A Caputo–Fabrizio (CF) form a fractional-system mathematical model for the fractional financial models of awareness is suggested. The fundamental attributes of the model are explored. The existence and uniqueness of the suggest fractional financial models of awareness solutions are given through the fixed point hypothesis. The non-number request subordinate gives progressively adaptable and more profound data about the multifaceted nature of the elements of the proposed partial budgetary models of mindfulness model than the whole number request models set up previously. In order to confirm the theoretical results and numerical simulations studies with Caputo derivative are offered.

scholarly journals On Hartree–Fock Systems

VLSI Design ◽  
1999 ◽  
Vol 9 (4) ◽  
pp. 357-364
Author(s):  
I. Gasser
Keyword(s):  
Existence And Uniqueness ◽  
Semiclassical Limit ◽  
Uniqueness Result ◽  
Nonlinear Schrödinger ◽  
Hartree Fock ◽  
Self Consistent ◽  
Nonlinear Schrödinger Systems ◽  
Schrödinger Systems

We show an existence and uniqueness result for mildly nonlinear Schrödinger systems of (self-consistent) Hartree–Fock form. We also shortly resume the already existing results on the semiclassical limit and the asymptotic and dispersive behavior of such systems.

Sign in / Sign up

Export Citation Format

Share Document