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Weak solvability of nonlinear elliptic equations involving variable exponents.

Authors :
Aberqi, Ahmed
Bennouna, Jaouad
Benslimane, Omar
Ragusa, Maria Alessandra
Source :
Discrete & Continuous Dynamical Systems - Series S; Jun2023, Vol. 16 Issue 6, p1-16, 16p
Publication Year :
2023

Abstract

We are concerned with the study of the existence and multiplicity of solutions for Dirichlet boundary value problems, involving the $ (p(m), \, q(m))- $ equation and the nonlinearity is superlinear but does not fulfil the Ambrossetti-Rabinowitz condition in the framework of Sobolev spaces with variable exponents in a complete manifold. The main results are proved using the mountain pass theorem and Fountain theorem with Cerami sequences. Moreover, an example of a $ (p(m), \, q(m)) $ equation that highlights the applicability of our theoretical results is also provided. Note: The second old affiliation of fourth author has been removed. The Acknowledgments' section has been updated. [ABSTRACT FROM AUTHOR]

Details

Language :
English
ISSN :
19371632
Volume :
16
Issue :
6
Database :
Complementary Index
Journal :
Discrete & Continuous Dynamical Systems - Series S
Publication Type :
Academic Journal
Accession number :
164876999
Full Text :
https://doi.org/10.3934/dcdss.2022105