On a Class of Elliptic (p, q)-Kirchhoff Type Systems with Multiple Parameters

Saleh Shakeri ()
Additional contact information
Saleh Shakeri: Islamic Azad University

Annals of Data Science, 2021, vol. 8, issue 4, No 8, 813-822

Abstract: Abstract This article concerns the existence of positive solutions for elliptic (p, q)-Kirchhoff type systems with multiple parameters. Our approach is based on the method of sub and super-solutions. The concepts of sub- and super-solution were introduced by Nagumo (Proc Phys-Math Soc Jpn19:861–866, 1937) in 1937 who proved, using also the shooting method, the existence of at least one solution for a class of nonlinear Sturm-Liouville problems. In fact, the premises of the sub- and super-solution method can be traced back to Picard. He applied, in the early 1880s, the method of successive approximations to argue the existence of solutions for nonlinear elliptic equations that are suitable perturbations of uniquely solvable linear problems. This is the starting point of the use of sub- and super-solutions in connection with monotone methods. Picard’s techniques were applied later by Poincaré (J Math Pures Appl 4:137–230, 1898) in connection with problems arising in astrophysics. We refer to Rădulescu (Qualitative analysis ofnonlinear elliptic partial differential equations: monotonicity, analytic, and variational methods, contemporary mathematics and its applications, Hindawi Publishing Corporation, New York, 2008).

Keywords: Elliptic systems; Sub and supersolutions; p-Laplacian; Sublinear; multiparameter; Positive solutions; Infinite semipositone; Existence; 35J60; 35j50 (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s40745-020-00317-6 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:aodasc:v:8:y:2021:i:4:d:10.1007_s40745-020-00317-6

Ordering information: This journal article can be ordered from
https://www.springer ... gement/journal/40745

DOI: 10.1007/s40745-020-00317-6

Access Statistics for this article

Annals of Data Science is currently edited by Yong Shi

More articles in Annals of Data Science from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().