Landesman-Lazer conditions for systems involving twist and positively homogeneous Hamiltonian systems

2024/07/11 by Natnael Gezahegn Mamo, Mamo, Natnael Gezahegn, Wahid Ullah +1
Computer Science · #34B15 #34C25 #Advanced Mathematical Modeling in Engineering #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2407.08389

openalex publication_date 2024/07/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We present multiplicity results for the periodic and Neumann-type boundary value problems associated with coupled Hamiltonian systems. For the periodic problem, we couple a system having twist condition with another one whose nonlinearity lies between the gradients of two positive and positively 2-homogeneous Hamiltonain functions. Concerning the Neumann-type problem, we treat the same system without any twist assumption. We examine the cases of nonresonance, simple resonance, and double resonance by imposing some kind of Landesman--Lazer conditions.

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