ABSTRACT
Let (M, g) be a complete noncompact Riemannian manifold
. In this paper, a fixed point result and a version of the Trudinger–Moser inequality are employed to establish sufficient conditions for the existence of solutions for quasilinear nonhomogeneous elliptic equation of the type
Here the function V(x) can change sign, f(x, u) is possibly discontinuous and can enjoy exponential critical growth and h belongs to the dual of an appropriated function space.
Acknowledgements
The author would like to thank the referees for the careful review and the valuable comments, which provided insights that helped improve the paper. The author also would like to thank Princeton University, for its hospitality while part of this work was completed, and the Federal University of Paraíba for supporting his long term visit to Princeton University during the academic year 2017–2018.
Notes
No potential conflict of interest was reported by the author.