Search results for "solutions"
showing 10 items of 757 documents
Regularity properties of tug-of-war games and normalized equations
2017
Oscillation of Second-Order Neutral Differential Equations
2013
Author's version of an article in the journal: Funkcialaj Ekvacioj. Also available from the publisher at: http://www.math.kobe-u.ac.jp/~fe/ We study oscillatory behavior of a class of second-order neutral differential equations relating oscillation of these equations to existence of positive solutions to associated first-order functional differential inequalities. Our assumptions allow applications to differential equations with both delayed and advanced arguments, and not only. New theorems complement and improve a number of results reported in the literature. Two illustrative examples are provided.
Two positive solutions for a nonlinear parameter-depending algebraic system
2021
The existence of two positive solutions for a nonlinear parameter-depending algebraic system is investigated. The main tools are a finite dimensional version of a two critical point theorem and a recent weak-strong discrete maximum principle.
Estimates of the modeling error generated by homogenization of an elliptic boundary value problem
2016
Erworben im Rahmen der Schweizer Nationallizenzen (http://www.nationallizenzen.ch)
Water Dynamics in Biological Systems investigated using Neutron Scattering Techniques
Living systems can not survive in absence of the water environments which play a fundamental role in living functions. Thus in the scienti?c community many studies were and are addressed to characterize water and its dynamics properties in biological systems. However, a clear description of water in such systems has been not reached yet. In fact, the investigations performed with di?erent techniques - those based on Nuclear Magnetic Resonance or those based on Neutron Scattering - look at di?erent di?usive motions and interactions water-biomolecules, leading controversial results and hence generating many debates between scientists. In this thesis we support the idea that two water populati…
Renormalized solutions on quasi open sets with nonhomogeneous boundary values
2006
8-parameter solutions of fifth order to the Johnson equation
2019
We give different representations of the solutions of the Johnson equation with parameters. First, an expression in terms of Fredholm determinants is given; we give also a representation of the solutions written as a quotient of wronskians of order 2N. These solutions of order N depend on 2N − 1 parameters. When one of these parameters tends to zero, we obtain N order rational solutions expressed as a quotient of two polyno-mials of degree 2N (N +1) in x, t and 4N (N +1) in y depending on 2N −2 parameters. Here, we explicitly construct the expressions of the rational solutions of order 5 depending on 8 real parameters and we study the patterns of their modulus in the plane (x, y) and their …
From first to fourth order rational solutions to the Boussinesq equation
2020
Rational solutions to the Boussinesq equation are constructed as a quotient of two polynomials in x and t. For each positive integer N , the numerator is a polynomial of degree N (N + 1) − 2 in x and t, while the denominator is a polynomial of degree N (N + 1) in x and t. So we obtain a hierarchy of rational solutions depending on an integer N called the order of the solution. We construct explicit expressions of these rational solutions for N = 1 to 4.