C. Martinez, A. Martinez, G. Bressan, E. V. Castelani, Roberto Molina de Souza
{"title":"具有非线性边界条件的四阶方程的多重解:理论和数值方面","authors":"C. Martinez, A. Martinez, G. Bressan, E. V. Castelani, Roberto Molina de Souza","doi":"10.7153/DEA-2019-11-15","DOIUrl":null,"url":null,"abstract":". We consider in this work the fourth order equation with nonlinear boundary condi- tions. We present the result for the existence of multiple solutions based on the Avery-Peterson fi xed-point theorem. This work is also a study for numerical solutions based on the Levenberg- Maquardt method with a heuristic strategy for initial points that proposes to numerically deter-mine multiple solutions to the problem addressed.","PeriodicalId":51863,"journal":{"name":"Differential Equations & Applications","volume":null,"pages":null},"PeriodicalIF":0.7000,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"Multiple solutions for a fourth order equation with nonlinear boundary conditions: theoretical and numerical aspects\",\"authors\":\"C. Martinez, A. Martinez, G. Bressan, E. V. Castelani, Roberto Molina de Souza\",\"doi\":\"10.7153/DEA-2019-11-15\",\"DOIUrl\":null,\"url\":null,\"abstract\":\". We consider in this work the fourth order equation with nonlinear boundary condi- tions. We present the result for the existence of multiple solutions based on the Avery-Peterson fi xed-point theorem. This work is also a study for numerical solutions based on the Levenberg- Maquardt method with a heuristic strategy for initial points that proposes to numerically deter-mine multiple solutions to the problem addressed.\",\"PeriodicalId\":51863,\"journal\":{\"name\":\"Differential Equations & Applications\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2019-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Differential Equations & Applications\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.7153/DEA-2019-11-15\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Differential Equations & Applications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.7153/DEA-2019-11-15","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
Multiple solutions for a fourth order equation with nonlinear boundary conditions: theoretical and numerical aspects
. We consider in this work the fourth order equation with nonlinear boundary condi- tions. We present the result for the existence of multiple solutions based on the Avery-Peterson fi xed-point theorem. This work is also a study for numerical solutions based on the Levenberg- Maquardt method with a heuristic strategy for initial points that proposes to numerically deter-mine multiple solutions to the problem addressed.