{"title":"Landesman-Lazer conditions for systems involving twist and positively homogeneous Hamiltonian systems","authors":"Natnael Gezahegn Mamo, Wahid Ullah","doi":"arxiv-2407.08389","DOIUrl":null,"url":null,"abstract":"We present multiplicity results for the periodic and Neumann-type boundary\nvalue problems associated with coupled Hamiltonian systems. For the periodic\nproblem, we couple a system having twist condition with another one whose\nnonlinearity lies between the gradients of two positive and positively\n2-homogeneous Hamiltonain functions. Concerning the Neumann-type problem, we\ntreat the same system without any twist assumption. We examine the cases of\nnonresonance, simple resonance, and double resonance by imposing some kind of\nLandesman--Lazer conditions.","PeriodicalId":501145,"journal":{"name":"arXiv - MATH - Classical Analysis and ODEs","volume":"28 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Classical Analysis and ODEs","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2407.08389","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
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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