{"title":"Lyapunov-type inequalities for third order nonlinear equations","authors":"Brian C. Behrens, Sougata Dhar","doi":"10.7153/dea-2022-14-18","DOIUrl":null,"url":null,"abstract":". We derive Lyapunov-type inequalities for general third order nonlinear equations in- volving multiple ψ -Laplacian operators of the form where ψ 2 and ψ 1 are odd, increasing functions, ψ 2 is super-multiplicative, ψ 1 is sub-multiplicative, and 1 ψ 1 is convex, and f is a continuous function which satisfies a sign condition. Our results utilize q + and q − , as opposed to | q | which appears in most results in the literature. Addi- tionally, these new inequalities generalize previously obtained results, and the proofs utilize a different technique than most other works in the literature. Furthermore, using the obtained in- equalities, we obtain a constraint on the location of the maximum of a solution, properties of oscillatory solutions, and an upper bound for the number of zeroes.","PeriodicalId":179999,"journal":{"name":"Differential Equations & Applications","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2022-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Differential Equations & Applications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.7153/dea-2022-14-18","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 derive Lyapunov-type inequalities for general third order nonlinear equations in- volving multiple ψ -Laplacian operators of the form where ψ 2 and ψ 1 are odd, increasing functions, ψ 2 is super-multiplicative, ψ 1 is sub-multiplicative, and 1 ψ 1 is convex, and f is a continuous function which satisfies a sign condition. Our results utilize q + and q − , as opposed to | q | which appears in most results in the literature. Addi- tionally, these new inequalities generalize previously obtained results, and the proofs utilize a different technique than most other works in the literature. Furthermore, using the obtained in- equalities, we obtain a constraint on the location of the maximum of a solution, properties of oscillatory solutions, and an upper bound for the number of zeroes.