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Existence of positive periodic solutions of an SEIR model with periodic coefficients

Tailei Zhang, Junli Liu, Zhidong Teng (2012)

Applications of Mathematics

An SEIR model with periodic coefficients in epidemiology is considered. The global existence of periodic solutions with strictly positive components for this model is established by using the method of coincidence degree. Furthermore, a sufficient condition for the global stability of this model is obtained. An example based on the transmission of respiratory syncytial virus (RSV) is included.

Existence of positive solution of a singular partial differential equation

Shu Qin Zhang (2008)

Mathematica Bohemica

Motivated by Vityuk and Golushkov (2004), using the Schauder Fixed Point Theorem and the Contraction Principle, we consider existence and uniqueness of positive solution of a singular partial fractional differential equation in a Banach space concerning with fractional derivative.

Existence of positive solutions for a class of arbitrary order boundary value problems involving nonlinear functionals

Kyriakos G. Mavridis (2014)

Annales Polonici Mathematici

We give conditions which guarantee the existence of positive solutions for a variety of arbitrary order boundary value problems for which all boundary conditions involve functionals, using the well-known Krasnosel'skiĭ fixed point theorem. The conditions presented here deal with a variety of problems, which correspond to various functionals, in a uniform way. The applicability of the results obtained is demonstrated by a numerical application.

Existence of positive solutions for a class of higher order neutral functional differential equations

Satoshi Tanaka (2001)

Czechoslovak Mathematical Journal

The higher order neutral functional differential equation d n d t n x ( t ) + h ( t ) x ( τ ( t ) ) + σ f t , x ( g ( t ) ) = 0 ( 1 ) is considered under the following conditions: n ≥ 2 , σ = ± 1 , τ ( t ) is strictly increasing in t ∈ [ t 0 , ∞ ) , τ ( t ) < t for t ≥ t 0 , lim t → ∞ τ ( t ) = ∞ , lim t → ∞ g ( t ) = ∞ , and f ( t , u ) is nonnegative on [ t 0 , ∞ ) × ( 0 , ∞ ) and nondecreasing in u ∈ ( 0 , ∞ ) . A necessary and sufficient condition is derived for the existence of certain positive solutions of (1).

Existence of positive solutions for a fractional boundary value problem with lower-order fractional derivative dependence on the half-line

Amina Boucenna, Toufik Moussaoui (2014)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

The aim of this paper is to study the existence of solutions to a boundary value problem associated to a nonlinear fractional differential equation where the nonlinear term depends on a fractional derivative of lower order posed on the half-line. An appropriate compactness criterion and suitable Banach spaces are used and so a fixed point theorem is applied to obtain fixed points which are solutions of our problem.

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