Existence of Positive Solutions of Higher Order Nonlinear Neutral Differential Equations

Existence of positive solutions of higher-order nonlinear neutral equations

where n ≥  is an integer, τ > , σ ≥ , d > c ≥ , b > a ≥ , r, P ∈ C([t,∞), (,∞)), P ∈ C([t,∞)× [a,b], (,∞)), Q ∈ C([t,∞), (,∞)), Q ∈ C([t,∞)× [c,d], (,∞)), f ∈ C(R,R), f is a nondecreasing function with xf (x) > , x = . The motivation for the present work was the recent work of Culáková et al. [] in which the second-order neutral nonlinear differential equation of the form [ ...

Existence of nonoscillatory solutions of higher-order neutral differential equations with positive and negative coefficients

Throughout this paper, the following conditions are assumed to hold. () n≥  is a positive integer, r ∈ C([t,∞),R+),  < a < b, τ > , σ > ; () p ∈ C([t,∞)× [a,b],R), q ∈ C([t,∞),R+), q ∈ C([t,∞),R+), h ∈ C([t,∞),R); () (u) is a continuously increasing real function with respect to u defined on R, and –(u) satisfies the local Lipschitz condition; () gi ∈ C(R,R), gi(u) satisfy the l...

Existence and Iterative Algorithms of Positive Solutions for a Higher Order Nonlinear Neutral Delay Differential Equation

and Applied Analysis 3 (d) if ∫+∞ c ∫ +∞ u uG(s, u)ds du < +∞, then ∞ ∑ j=1 ∫ +∞ t+jτ ∫ +∞ u G (s, u) ds du ≤ 1 τ ∫ +∞ t+τ ∫ +∞ u uG (s, u) ds du < +∞, ∀t ≥ c. (10) Proof. Let [t] denote the largest integral number not exceeding t ∈ R. Note that lim r→+∞ [(r − c) /τ] + 1 r = 1 τ , (11) c + nτ ≤ r < c + (n + 1) τ ⇐⇒ n ≤ r − c τ < n + 1, ∀n ∈ N0. (12) Clearly (12) means that ∞ ∑ j=0 ∫ +∞

Existence for Eventually Positive Solutions of High-Order Nonlinear Neutral Differential Equations with Distributed Delay

Existence and multiplicity of positive solutions for a coupled system of perturbed nonlinear fractional differential equations

In this paper, we consider a coupled system of nonlinear fractional differential equations (FDEs), such that both equations have a particular perturbed terms. Using emph{Leray-Schauder} fixed point theorem, we investigate the existence and multiplicity of positive solutions for this system.