THE EXISTENCE OF ONE NON-TRIVIAL WEAK SOLUTION OF GENERALIZED YAMABE EQUATIONS

摘要

In this work, we study the nonlinear problem on compact d-dimensional (d >= 3) Riemannian manifolds with respect to absence of boundary. The existence of one non-trivial weak solution is established, and its application to solve Emden-Fowler equations which contain infinity nonlinear terms. We also introduce an example to illustrate the results obtained, which can be applied to many of the problems resulting in astrophysics, conformal Riemannian geometry, gas combustion, isothermal stationary gas sphere and in the theory of thermionic emission.