Attractor bifurcation for FKPP type equation with periodic boundary condition

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 ...

Bifurcation for Second-Order Hamiltonian Systems with Periodic Boundary Conditions

Through variational methods, we study nonautonomous systems of second-order ordinary differential equations with periodic boundary conditions. First, we deal with a nonlinear system, depending on a function u, and prove that the set of bifurcation points for the solutions of the system is not σ-compact. Then, we deal with a linear system depending on a real parameter λ > 0 and on a function u, ...

On the Cauchy Problem for the Derivative Nonlinear Schrödinger Equation with Periodic Boundary Condition

It is shown that the Cauchy problem associated to the derivative nonlinear Schrödinger equation ∂tu − i∂ xu = λ∂x(|u| u) is locally well-posed for initial data u(0) ∈ H(T), if s ≥ 1 2 and λ is real. The proof is based on an adaption of the gauge transformation to periodic functions and sharp multi-linear estimates for the gauge equivalent equation in Fourier restriction norm spaces. By the use ...

Hopf bifurcation in a reaction–diffusion equation with distributed delay and Dirichlet boundary condition

The stability and Hopf bifurcation of the positive steady state to a general scalar reaction–diffusion equation with distributed delay and Dirichlet boundary condition are investigated in this paper. The time delay follows a Gamma distribution function. Through analyzing the corresponding eigenvalue problems, we rigorously show that Hopf bifurcations will occur when the shape parameter n ≥ 1, a...

Positive Solutions for Nonlinear Differential Equations with Periodic Boundary Condition