Multiple Solutions Of Boundary Value Problems Research Articles

Multiple Solutions of Boundary-Value Problems for Hamiltonian Systems

We consider two-point boundary-value problems for a Hamiltonian system of the form x′ = f(k, y), y′ = g(x, 𝜆), where k and 𝜆 are parameters. The numbers of solutions, both positive and oscillatory, for the boundary-value problems are estimated. Our main tool is the analysis of the phase plane combined with the evaluation of time-map functions. The bifurcation diagram and solution curves are constructed for the Hamiltonian system. We also present examples illustrating the bifurcations with respect to the parameters k and 𝜆:

Multiple solutions of boundary-value problems for impulsive differential equations

In this paper, we investigate the existence of multiple solutions to a second-order Dirichlet boundary-value problem with impulsive effects. The proof is based on critical point theorems. Copyright © 2011 John Wiley & Sons, Ltd.