TY - JOUR
T1 - On variational methods for interval-valued functions with some applications
AU - Zhang, Chuang liang
AU - Huang, Nan jing
AU - O'Regan, Donal
N1 - Publisher Copyright:
© 2022 Elsevier Ltd
PY - 2023/2
Y1 - 2023/2
N2 - In this paper, we introduce the concept of sequential weak lower semicontinuity of interval-valued functions defined on a Banach space. We focus on the direct methods of the calculus of variations for interval-valued functions and extend some well-known results of F.E. Browder from scalar results to interval-valued cases. Moreover, we obtain some new results on the Palais–Smale condition and the coercivity for interval-valued functions. Finally, we apply the obtained results to interval-valued integral functions, to interval-valued optimal control problems, and to variational problems for interval-valued functions.
AB - In this paper, we introduce the concept of sequential weak lower semicontinuity of interval-valued functions defined on a Banach space. We focus on the direct methods of the calculus of variations for interval-valued functions and extend some well-known results of F.E. Browder from scalar results to interval-valued cases. Moreover, we obtain some new results on the Palais–Smale condition and the coercivity for interval-valued functions. Finally, we apply the obtained results to interval-valued integral functions, to interval-valued optimal control problems, and to variational problems for interval-valued functions.
KW - Calculus of variations
KW - Coercivity
KW - Interval-valued function
KW - Palais–Smale condition
KW - Sequential weak lower semicontinuity
UR - https://www.scopus.com/pages/publications/85145435569
U2 - 10.1016/j.chaos.2022.113083
DO - 10.1016/j.chaos.2022.113083
M3 - Article
AN - SCOPUS:85145435569
SN - 0960-0779
VL - 167
JO - Chaos, Solitons and Fractals
JF - Chaos, Solitons and Fractals
M1 - 113083
ER -