Existence of Noncontinuable Solutions

On Noncontinuable Solutions of Differential Equations with Delay

(1) where n ≥ 2, f is a continuous function defined on R+ × R , R+ = [0,∞), R = (−∞,∞), τi ∈ C (R+) and τi(t) ≤ t for t ∈ R+ and i = 0, 1, . . . , n− 1 . We will suppose for the simplicity that inf t∈R+ τi(t) > −∞ for i = 0, 1, . . . , n − 1. Note, that C(I), s ∈ {0, 1, . . .}, I ⊂ R+ is the set of continuous functions on I that have continuous derivatives up to the order s. A special case of e...

Large linear manifolds of noncontinuable boundary - regular holomorphic functions ✩

ON THE EXISTENCE OF PERIODIC SOLUTIONS FOR CERTAIN NON-LINEAR DIFFERENTIAL EQUATIONS

Here we consider some non-autonomous ordinary differential equations of order n and present some results and theorems on the existence of periodic solutions for them, which are sufficient conditions, section 1. Also we include generalizations of these results to vector differential equations and examinations of some practical examples by numerical simulation, section 2. For some special cases t...

Differential Delayed Equations - Asymptotic Behavior of Solutions and Positive Solutions

Brief Summary of Basic Notions For a b R , ∈ , a b < , let ([ ] ) n C a b R , , be the Banach space of the continuous functions from the interval [ ] a b , into n R equipped with the supremum norm | ⋅ | . In the case 0 a r = − < , 0 b = , we shall denote this space as r C , that is, ([ 0] ) n r C C r R := − , , and put 0 sup ( ) r r σ φ φ σ − ≤ ≤ || || = | | for r C φ∈ . If R σ ∈ , 0 A ≥ and ([...

$L^p$-existence of mild solutions of fractional differential equations in Banach space

We study the existence of mild solutions for semilinear fractional differential equations with nonlocal initial conditions in $L^p([0,1],E)$, where $E$ is a separable Banach space. The main ingredients used in the proof of our results are measure of noncompactness, Darbo and Schauder fixed point theorems. Finally, an application is proved to illustrate the results of this work.