Existence and uniqueness of periodic solutions for some nonlinear fractional pantograph differential equations with $$\psi $$-Caputo derivative

The aim of this paper is to study the existence and uniqueness of periodic solutions for a certain type of nonlinear fractional pantograph differential equation with a $$\psi $$ ψ -Caputo derivative. The proofs are based on the coincidence degree theory of Mawhin. To show the efficiency of the results, some illustrative examples are included.

On the Solvability of a Resonant Third-Order Integral m-Point Boundary Value Problem on the Half-Line

In this work, the existence of at least one solution for the following third-order integral and m -point boundary value problem on the half-line at resonance ρ t u ′ t ″ = w t , u t , u ′ t , u ″ t , t ∈ 0 , ∞ , u 0 = ∑ j = 1 m α j ∫ 0 η j u t d t , u ′ 0 = 0 , lim t ⟶ ∞ ρ t u ′ t ′ = 0 , will be investigated. The Mawhin’s coincidence degree theory will be used to obtain existence results while an example will be used to validate the result obatined.

On the Existence of Coupled Fractional Jerk Equations with Multi-Point Boundary Conditions

By coincidence degree theory due to Mawhin, some sufficient conditions for the existence of solution for a class of coupled jerk equations with multi-point conditions are established. The new existence results have not yet been reported before. Novel coupled fractional jerk equations with resonant boundary value conditions are discussed in detail for the first time. Our work is interesting and complements known results.

Existence of Homoclinic Orbits for a Singular Differential Equation Involving p-Laplacian

The efficient conditions guaranteeing the existence of homoclinic solutions to second-order singular differential equation with p-Laplacian ϕpx′t′+fx′t+gxt+ht/1−xt=et are established in the paper. Here, ϕps=sp−2s,p>1,f,g,h,e∈Cℝ,ℝ with ht+T=ht. The approach is based on the continuation theorem for coincidence degree theory.

Existence, Uniqueness and Exponential Stability of Periodic Solution for Discrete-Time Delayed BAM Neural Networks Based on Coincidence Degree Theory and Graph Theoretic Method

In this work, a general class of discrete time bidirectional associative memory (BAM) neural networks (NNs) is investigated. In this model, discrete and continuously distributed time delays are taken into account. By utilizing this novel method, which incorporates the approach of Kirchhoff’s matrix tree theorem in graph theory, Continuation theorem in coincidence degree theory and Lyapunov function, we derive a few sufficient conditions to ensure the existence, uniqueness and exponential stability of the periodic solution of the considered model. At the end of this work, we give a numerical simulation that shows the effectiveness of this work.

Strong singularities of attractive and repulsive type to 2n-order neutral differential equation

This paper is devoted to the existence of a positive periodic solution for a kind of 2n-order neutral differential equation with a singularity, where nonlinear term $g(t,x)$ g ( t , x ) has strong singularities of attractive and repulsive type at the origin. Our proof is based on coincidence degree theory.

Almost Periodic Sequence in a Discrete Logistic Equation

This paper is concerned with an almost periodic discrete logistic equation. By using thecontinuation theorem of Mawhin’s coincidence degree theory, this paper investigates theexistence and stability of a unique positive almost periodic sequence solution of the equation.These results generalize and improve the previous works, and they are easy to check. An examplewith a numerical simulation is also given to demonstrate the effectiveness of the results in this paper.