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arXiv · 2407.08389

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

Natnael Gezahegn Mamo·Wahid Ullah
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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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Natnael Gezahegn Mamo, Wahid Ullah. 2024-07-11. Landesman-Lazer conditions for systems involving twist and positively homogeneous Hamiltonian systems. https://arxiv.org/abs/2407.08389

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