Two homoclinic solutions for a nonperiodic fourth order differential equation with a perturbation

Periodic solutions of fourth-order delay differential equation

In this paper the periodic solutions of fourth order delay differential equation of the form $ddddot{x}(t)+adddot{x}(t)+f(ddot{x}(t-tau(t)))+g(dot{x}(t-tau(t)))+h({x}(t-tau(t)))=p(t)$  is investigated. Some new positive periodic criteria are given.  

periodic solutions of fourth-order delay differential equation

in this paper the periodic solutions of fourth order delay differential equation of the form $ddddot{x}(t)+adddot{x}(t)+f(ddot{x}(t-tau(t)))+g(dot{x}(t-tau(t)))+h({x}(t-tau(t)))=p(t)$  is investigated. some new positive periodic criteria are given.

Homoclinic Solutions for a Second-Order Nonperiodic Asymptotically Linear Hamiltonian Systems

and Applied Analysis 3 Note that the inequality (14) holds true with constantC = √ 2 if T ≥ 1/2 (see [9]). Subsequently, we may assume this condition is fulfilled. Consider a functional I : E T → R defined by

Homoclinic Solutions for Fourth Order Traveling Wave Equations

We consider homoclinic solutions of fourth order equations u ′′′′ + βu ′′ + Vu(u) = 0 in R , where V (u) is either the suspension bridge type V (u) = eu − 1 − u or SwiftHohenberg type V (u) = 1 4 (u2 − 1)2. For the suspension bridge type equation, we prove existence of a homoclinic solution for all β ∈ (0, β∗) where β∗ = 0.7427 · · · . For the Swift-Hohenberg type equation, we prove existence o...

A method for solving first order fuzzy differential equation