Homoclinic orbits for a singular second-order neutral differential equation

Homoclinic Solutions of Singular Nonautonomous Second-Order Differential Equations

Persistent Homoclinic Orbits for Nonlinear Schrödinger Equation Under Singular Perturbation

Existence of homoclinic orbits in the cubic nonlinear Schrödinger equation under singular perturbations is proved. Emphasis is placed upon the regularity of the semigroup eǫt∂ 2 x at ǫ = 0. This article is a substantial generalization of [3], and motivated by the effort of Dr. Zeng [9] [8]. The mistake of Zeng in [8] is corrected with a normal form transform approach. Both one and two unstable ...

Oscillation for a second-order neutral differential equation with impulses

We consider a certain type of second-order neutral delay differential systems and we establish two results concerning the oscillation of solutions after the system undergoes controlled abrupt perturbations (called impulses). As a matter of fact, some particular non-impulsive cases of the system are oscillatory already. Thus, we are interested in finding adequate impulse controls under which our...

On Fuzzy Solution for Exact Second Order Fuzzy Differential Equation

In the present paper, the analytical solution for an exact second order fuzzy initial value problem under generalized Hukuhara differentiability is obtained. First the solution of first order linear fuzzy differential equation under generalized Hukuhara differentiability is investigated using integration factor methods in two cases. The second based on the type of generalized Hukuhara different...

Homoclinic Orbits of the FitzHugh-Nagumo Equation: The Singular-Limit

The FitzHugh-Nagumo equation has been investigated with a wide array of different methods in the last three decades. Recently a version of the equations with an applied current was analyzed by Champneys, Kirk, Knobloch, Oldeman and Sneyd [5] using numerical continuation methods. They obtained a complicated bifurcation diagram in parameter space featuring a C-shaped curve of homoclinic bifurcati...