Generalized yamabe equations on riemannian manifolds and applications to Emden-Fowler problems

Published in: Quaestiones Mathematicae
Volume 43, issue 4, 2020 , pages: 547–567
DOI: 10.2989/16073606.2019.1583293
Author(s): David BarillaDepartment of Economics, Italy, Giuseppe CaristiDepartment of Economics, Italy, Shapour HeidarkhaniDepartment of Mathematics, Faculty of Sciences, Iran, Shahin MoradiDepartment of Mathematics, Faculty of Sciences, Iran


In this paper, we establish the existence of solutions and multiplicity properties for generalized Yamabe equations on Riemannian manifolds. Problems of this type arise in conformal Riemannian geometry, astrophysics, and in the theories of thermionic emission, isothermal stationary gas sphere, and gas combustion. The abstract results of this paper are illustrated with Emden-Fowler equations involving sublinear terms at infinity. Two examples reveal the analytic setting of this paper.

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