The existence of one non-trivial weak solution of generalized Yamabe equations

Miskolc Mathematical Notes

article

T. Bouali¹  R. Guefaifia²  A. Choucha³  S. Boulaaras⁴  M. Abdalla⁵ 

[1] Department of Mathematics, College of Sciences, Jazen University;Laboratory of Mathematics, Informatics and Systems, Larbi Tebessi University;Laboratory of Operator Theory and PDEs: Foundations and Applications, Department of Mathematics, Faculty of Exact Sciences, University of El Oued;Department of Mathematics, College of Sciences and Arts, ArRass, Qassim University;Mathematics Department, College of Science, King Khalid, University;Mathematics Department, Faculty of Science, South Valley University

关键词: Yamabe problem;    Emden-Fowler equation;    sublinear eigenvalue problem;    one nontrivial solutions;    Riemannian manifolds;   

DOI  :  10.18514/MMN.2022.3751

学科分类：数学（综合）

来源: Miskolci Egyetem

【 摘 要 】

In this work, we are interested to study the nonlinear problem on compact $d$-dimensional with respect to absence of ($d\geq 3$) Riemannian manifolds. The existence of one non-trivial weak solution is established, and its application to solve of Emden Fowler equations which contain at infinity nonlinear terms. We also introduced an example to illustrate the results obtained, which applies to many of the problems resulting in astrophysics, conformal Riemannian geometry, gas combustion, isothermal stationary gas sphere and in the theories of thermionic emission.

【 授权许可】

CC BY