Multiplicity results for boundary value problems associated with Hamiltonian systems

Speaker – Wahid Ullah (University of Trieste, Italy)

Abstract – In this talk, I will focus on the periodic and Neumann-type boundary value problems associated with Hamiltonian systems. I classify my presentation into three parts. In the first part, I will discuss some extensions of the higher dimension Poincar´e–Birkhoff theorem for coupled Hamiltonian systems. The systems we are coupling have completely different behaviours: the first one is a system with periodic Hamiltonian in the space variable, while the second one is either a system having generalized lower/upper solutions or a positively-(p, q)-homogeneous Hamiltonian system. In the second part of my talk, I will discuss some multiplicity results for Neumann-type boundary value problems. The final part of my talk is dedicated to my recent result concerning the multiplicity of solutions for Hamiltonian systems associated with mixed periodic and Neumann-type boundary conditions.

Time – 15:00, 29.4
Location – zoom
Zoom Meeting ID: 844 0594 7424 (Passcode: 076895)

References:
[1] A. Fonda and W. Ullah, Periodic solutions of Hamiltonian systems coupling twist with generalized lower/upper solutions, J. Differential Equations 379 (2024), 148–174.
[2] A. Fonda and W. Ullah, Periodic solutions of Hamiltonian systems coupling twist with an isochronous center, Differential Integral Equations, 37 (2024), 323–336.
[3] A. Fonda and W. Ullah, Boundary value problems associated with Hamiltonian systems coupled with positively-(p,q)-homogeneous systems, NoDEA Nonlinear Differential Equations Appl. 31 (2024), No. 41, 28 pp.
[4] W. Ullah, A multiplicity result for Hamiltonian systems with mixed periodic-type and Neumann-type boundary conditions, Preprint 2024.