{"title":"The second-order Cauchy problem in a scale of Banach spaces with vector-valued measures of noncompactness and an application to Kirchhoff equations","authors":"","doi":"10.23952/jnfa.2023.10","DOIUrl":null,"url":null,"abstract":". In the paper, by using Darbo-Sadovskii fixed point theorem for condensing operators on Fr ´ echet spaces with respect to vector-valued measure of noncompactness, we prove the existence results for the second-order Cauchy problem u (cid:48)(cid:48) ( t ) = f ( t , u ( t )) , t ∈ ( 0 , T ) , u ( 0 ) = u 0 , u (cid:48) ( 0 ) = u 1 , in a scale of Banach spaces. The result is applied to the Kirchhoff equations in Gevrey class.","PeriodicalId":44514,"journal":{"name":"Journal of Nonlinear Functional Analysis","volume":"41 1","pages":"0"},"PeriodicalIF":1.1000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Nonlinear Functional Analysis","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.23952/jnfa.2023.10","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
. In the paper, by using Darbo-Sadovskii fixed point theorem for condensing operators on Fr ´ echet spaces with respect to vector-valued measure of noncompactness, we prove the existence results for the second-order Cauchy problem u (cid:48)(cid:48) ( t ) = f ( t , u ( t )) , t ∈ ( 0 , T ) , u ( 0 ) = u 0 , u (cid:48) ( 0 ) = u 1 , in a scale of Banach spaces. The result is applied to the Kirchhoff equations in Gevrey class.
期刊介绍：
Journal of Nonlinear Functional Analysis focuses on important developments in nonlinear functional analysis and its applications with a particular emphasis on topics include, but are not limited to: Approximation theory; Asymptotic behavior; Banach space geometric constant and its applications; Complementarity problems; Control theory; Dynamic systems; Fixed point theory and methods of computing fixed points; Fluid dynamics; Functional differential equations; Iteration theory, iterative and composite equations; Mathematical biology and ecology; Miscellaneous applications of nonlinear analysis; Multilinear algebra and tensor computation; Nonlinear eigenvalue problems and nonlinear spectral theory; Nonsmooth analysis, variational analysis, convex analysis and their applications; Numerical analysis; Optimal control; Optimization theory; Ordinary differential equations; Partial differential equations; Positive operator inequality and its applications in operator equation spectrum theory and so forth; Semidefinite programming polynomial optimization; Variational and other types of inequalities involving nonlinear mappings; Variational inequalities.
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