INFINITE RESONANT SOLUTIONS AND TURNING POINTS IN A PROBLEM WITH UNBOUNDED BIFURCATION

Infinite Resonant Solutions and Turning Points in a Problem with Unbounded bifurcation

We consider an elliptic equation −∆u + u = 0 with nonlinear boundary conditions ∂u ∂n = λu + g(λ, x, u), where g(λ, x, s) s → 0, as |s| → ∞. In [1, 2] the authors proved the existence of unbounded branches of solutions near a Steklov eigenvalue of odd multiplicity and, among other things, provided tools to decide whether the branch is subcritical or supercritical. In this work we give condition...

The Uniqueness Theorem for the Solutions of Dual Equations of Sturm-Liouville Problems with Singular Points and Turning Points

In this paper, linear second-order differential equations of Sturm-Liouville type having a finite number of singularities and turning points in a finite interval are investigated. First, we obtain the dual equations associated with the Sturm-Liouville equation. Then, we prove the uniqueness theorem for the solutions of dual initial value problems.

Canard Solutions at Non-generic Turning Points

This paper deals with singular perturbation problems for vector fields on 2-dimensional manifolds. “Canard solutions” are solutions that, starting near an attracting normally hyperbolic branch of the singular curve, cross a “turning point” and follow for a while a normally repelling branch of the singular curve. Following the geometric ideas developed by Dumortier and Roussarie in 1996 for the ...

Existence of Unbounded Solutions for a Third-Order Boundary Value Problem on Infinite Intervals

Bifurcation of limit cycles from a quadratic reversible center with the unbounded elliptic separatrix

The paper is concerned with the bifurcation of limit cycles in general quadratic perturbations of a quadratic reversible and non-Hamiltonian system, whose period annulus is bounded by an elliptic separatrix related to a singularity at infinity in the poincar'{e} disk. Attention goes to the number of limit cycles produced by the period annulus under perturbations. By using the appropriate Picard...