New results for a class of quasilinear Schrödinger equations

Taib Talbi ()
Additional contact information
Taib Talbi: Higher Institute of Applied Sciences and Technology of Kairouan

Partial Differential Equations and Applications, 2025, vol. 6, issue 4, 1-18

Abstract: Abstract In this paper, we investigate a class of quasilinear Schrödinger equations involving the Laplacian, a potential function V(x), and a nonlinear term that depends on a function f(x, u). The variable x belongs to $$\mathbb {R}^N$$ R N , where $$N \ge 3$$ N ≥ 3 . We impose suitable conditions on the parameter $$\tau $$ τ (with $$\tau \ge 2$$ τ ≥ 2 ), the potential V (assumed to be continuous on $$\mathbb {R}^N$$ R N ), and the nonlinearity f (assumed to be locally defined with respect to u near the origin). Under these assumptions, we establish the existence of infinitely many solutions in a neighborhood of the origin. An example is provided to illustrate the applicability of the main theoretical results.

Keywords: Variational methods; Critical points; Quasilinear Schrödinger equation; 49J35; 35Q40; 81V10 (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s42985-025-00338-x 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:6:y:2025:i:4:d:10.1007_s42985-025-00338-x

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

DOI: 10.1007/s42985-025-00338-x

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 ().