MMN-3751

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

  • T. Bouali, Department of Mathematics, College of Sciences, Jazen University, P.O.Box 277, Jazen, Saudi Arabia and Laboratory of Mathematics, Informatics and Systems, Larbi Tebessi University, 12000, Tebessa, Algeria, tbouali@jazanu.edu.sa
  • R. Guefaifia, Laboratory of Mathematics, Informatics and Systems, Larbi Tebessi University, 12000, Tebessa, Algeria, rafik.guefaifia@univ-tebessa.dz
  • A. Choucha, Laboratory of Operator Theory and PDEs: Foundations and Applications, Department of Mathematics, Faculty of Exact Sciences, University of El Oued, Box.789, El Oued 39000, Algeria, abdelbaki.choucha@gmail.com
  • S. Boulaaras, Department of Mathematics, College of Sciences and Arts, ArRass, Qassim University, Saudi Arabia, s.boularas@qu.edu.sa
  • M. Abdalla, Mathematics Department, College of Science, King Khalid, University, Abha 61413, Saudi Arabia and Mathematics Department, Faculty of Science, South Valley University, Qena 83523, Egypt, moabdalla@kku.edu.sa

Abstract

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.


Vol. 23 (2022), No. 1, pp. 117-129
DOI: 10.18514/MMN.2022.3751


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