Existence of positive solutions for a neutral differential equation with positive and negative coefficients

Existence of positive solutions for a boundary value problem of a nonlinear fractional differential equation

This paper presents conditions for the existence and multiplicity of positive solutions for a boundary value problem of a nonlinear fractional differential equation. We show that it has at least one or two positive solutions. The main tool is Krasnosel'skii fixed point theorem on cone and fixed point index theory.

Existence of Nonoscillatory and Oscillatory Solutions of Neutral Differential Equations with Positive and Negative Coefficients

In this paper, we study the existence of oscillatory and nonoscillatory solutions of neutral differential equations of the form ( x(t)− cx(t− r))′ ± (P (t)x(t− θ)−Q(t)x(t− δ)) = 0 where c > 0, r > 0, θ > δ 0 are constants, and P , Q ∈ C( +, +). We obtain some sufficient and some necessary conditions for the existence of bounded and unbounded positive solutions, as well as some sufficient condit...

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 of positive solutions of a third order nonlinear differential equation with positive and negative terms

Positive Solutions of Neutral Delay Differential Equation

Neutral delay differential equations contain the derivative of the unknown function both with and without delays. Some new phenomena can appear, hence the theory of neutral delay differential equations is even more complicated than the theory of non-neutral delay equations. The oscillatory behavior of the solutions of neutral systems is of importance in both the theory and applications, such as...