{"title":"三阶非线性方程的lyapunov型不等式","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":"{\"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}","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}
Lyapunov-type inequalities for third order nonlinear equations
. 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.