Boundary layer behavior in perturbed second-order systems

Second-order analysis in polynomially perturbed reversible quadratic Hamiltonian systems

We study degree n polynomial perturbations of quadratic reversible Hamiltonian vector fields with one center and one saddle point. It was recently proved that if the first Poincaré–Pontryagin integral is not identically zero, then the exact upper bound for the number of limit cycles on the finite plane is n− 1. In the present paper we prove that if the first Poincaré–Pontryagin function is iden...

A hybrid method for singularly perturbed delay boundary value problems exhibiting a right boundary layer

The aim of this paper is to present a numerical method for singularly perturbed convection-diffusion problems with a delay. The method is a combination of the asymptotic expansion technique and the reproducing kernel method (RKM). First an asymptotic expansion for the solution of the given singularly perturbed delayed boundary value problem is constructed. Then the reduced regular delayed diffe...

Nvestigation of a Boundary Layer Problem for Perturbed Cauchy-Riemann Equation with Non-local Boundary Condition

Boundary layer problems (Singular perturbation problems) more have been applied for ordinary differential equations. While this theory for partial differential equations have many applications in several fields of physics and engineering. Because of complexity of limit and boundary behavior of the solutions of partial differential equations these problems considered less than ordinary case. In ...

Asymptotic analysis of second-order boundary layer correctors

Multiple Periodic Solutions for Perturbed Second-order Impulsive Hamiltonian Systems

The existence of three distinct periodic solutions for a class of perturbed impulsive Hamiltonian systems is established. The techniques used in the proofs are based on variational methods. AMS Subject Classification: 34B15