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Global solvability criteria for quaternionic Riccati equations

G.A. Grigorian (2021)

Archivum Mathematicum

Some global existence criteria for quaternionic Riccati equations are established. Two of them are used to prove a completely non conjugation theorem for solutions of linear systems of ordinary differential equations.

Global stability of steady solutions for a model in virus dynamics

Hermano Frid, Pierre-Emmanuel Jabin, Benoît Perthame (2003)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

We consider a simple model for the immune system in which virus are able to undergo mutations and are in competition with leukocytes. These mutations are related to several other concepts which have been proposed in the literature like those of shape or of virulence – a continuous notion. For a given species, the system admits a globally attractive critical point. We prove that mutations do not affect this picture for small perturbations and under strong structural assumptions. Based on numerical...

Global Stability of Steady Solutions for a Model in Virus Dynamics

Hermano Frid, Pierre-Emmanuel Jabin, Benoît Perthame (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

We consider a simple model for the immune system in which virus are able to undergo mutations and are in competition with leukocytes. These mutations are related to several other concepts which have been proposed in the literature like those of shape or of virulence – a continuous notion. For a given species, the system admits a globally attractive critical point. We prove that mutations do not affect this picture for small perturbations and under strong structural assumptions. Based on numerical...

Global structure of positive solutions for superlinear 2 m th-boundary value problems

Ruyun Ma, Yulian An (2010)

Czechoslovak Mathematical Journal

We consider boundary value problems for nonlinear 2 m th-order eigenvalue problem ( - 1 ) m u ( 2 m ) ( t ) = λ a ( t ) f ( u ( t ) ) , 0 < t < 1 , u ( 2 i ) ( 0 ) = u ( 2 i ) ( 1 ) = 0 , i = 0 , 1 , 2 , , m - 1 . where a C ( [ 0 , 1 ] , [ 0 , ) ) and a ( t 0 ) > 0 for some t 0 [ 0 , 1 ] , f C ( [ 0 , ) , [ 0 , ) ) and f ( s ) > 0 for s > 0 , and f 0 = , where f 0 = lim s 0 + f ( s ) / s . We investigate the global structure of positive solutions by using Rabinowitz’s global bifurcation theorem.

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