An MP-Newton method for finding orthogonal-max type critical points and its application for calculating multiple solutions of semilinear elliptic equations: part I—method

Xudong Yao ()
Additional contact information
Xudong Yao: Shanghai Normal University

Partial Differential Equations and Applications, 2024, vol. 5, issue 3, 1-26

Abstract: Abstract ln Li and Zhou (SIAM J Sci Comput 23:840–865, 2001), a minimax method for computing multiple solutions of semilinear elliptic equation by calculating critical points of its energy function is presented. But, the method is slow and can find limited amount of solutions. In this paper, a new general characterization, orthogonal-max characterization, for critical points of the energy function is suggested. An MP-Newton method for finding orthogonal-max type critical points is designed through analyzing how the minimax method works. The new method becomes fast and able to calculate more solutions of semilinear elliptic equation. Numerical experiment confirms these two progresses. In addition, the MP-Newton method inherits the advantages of the minimax method. Finally, a convergence result for the method is established.

Keywords: MP-Newton method; Orthogonal-max type critical points; Convergence; 49M15; 65K10; 49J50; 58E05 (search for similar items in EconPapers)
Date: 2024
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s42985-024-00284-0 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:pardea:v:5:y:2024:i:3:d:10.1007_s42985-024-00284-0

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/42985/

DOI: 10.1007/s42985-024-00284-0

Access Statistics for this article

Partial Differential Equations and Applications is currently edited by Zhitao Zhang

More articles in Partial Differential Equations and Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().