THE SECOND-ORDER CAUCHY PROBLEM IN A SCALE OF BANACH SPACES WITH VECTOR-VALUED MEASURES OF NONCOMPACTNESS AND AN APPLICATION TO KIRCHHOFF EQUATIONS

被引：0

作者：

Pham, Van Hien ^{[1
]}

机构：

[1] Ho Chi Minh City Univ Technol & Educ, Fac Appl Sci, Ho Chi Minh City, Vietnam

来源：

JOURNAL OF NONLINEAR FUNCTIONAL ANALYSIS | 2023年 / 2023卷

关键词：

Condensing operator; Kirchhoff equation; Measures of noncompactness; Scale of Banach spaces;

D O I：

10.23952/jnfa.2023.10

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In the paper, by using Darbo-Sadovskii fixed point theorem for condensing operators on Frechet spaces with respect to vector-valued measure of noncompactness, we prove the existence results for the second-order Cauchy problem u''(t) = f(t,u(t)), t E (0,T), u(0) = u0, u'(0) = u1, in a scale of Banach spaces. The result is applied to the Kirchhoff equations in Gevrey class.

引用

页数：11

共 50 条

[1] THE SECOND-ORDER CAUCHY PROBLEM IN A SCALE OF BANACH SPACES WITH VECTOR-VALUED MEASURES OF NONCOMPACTNESS AND AN APPLICATION TO KIRCHHOFF EQUATIONS
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[J]. Journal of Nonlinear Functional Analysis, 2023, 2023 (01):
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