Two Nontrivial Solutions for a Nonhomogeneous Quasilinear Elliptic System With Sign‐Changing Weight Functions

ABSTRACT We are interested in looking for two nontrivial solutions for a class of nonhomogeneous quasilinear elliptic system with sign‐changing weight functions and concave‐convex nonlinearities on the bounded domain. This kind of quasilinear elliptic system arises from nonlinear optics, whose featu...

Full description

Saved in:
Bibliographic Details
Published inMathematical methods in the applied sciences Vol. 48; no. 12; pp. 11836 - 11849
Main Authors Qi, Wanting, Zhang, Xingyong
Format Journal Article
LanguageEnglish
Published Freiburg Wiley Subscription Services, Inc 01.08.2025
Subjects
concave‐convex nonlinearities
Differential equations
Ekeland's variational principle
mountain pass theorem
nonhomogeneous quasilinear elliptic system
Nonlinear optics
Nonlinearity
Operators (mathematics)
Weighting functions
Online AccessGet full text

Cover

More Information
Summary:ABSTRACT We are interested in looking for two nontrivial solutions for a class of nonhomogeneous quasilinear elliptic system with sign‐changing weight functions and concave‐convex nonlinearities on the bounded domain. This kind of quasilinear elliptic system arises from nonlinear optics, whose feature is that its differential operator depends on not only ∇u$$ \nabla u $$ but also u$$ u $$. Employing the mountain pass theorem and Ekeland's variational principle as the major tools, we show that the system has at least one nontrivial solution of positive energy and one nontrivial solution of negative energy, respectively.
Bibliography:Funding
This work is supported by Yunnan Fundamental Research Projects in China (grant no: 202301AT070465) and Xingdian Talent Support Program for Young Talents of Yunnan Province in China.
ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:0170-4214
1099-1476
DOI:10.1002/mma.10997