Generalized Yamabe equations on Riemannian manifolds and applications to Emden-Fowler problems. (English) Zbl 1441.35120
This article discusses the existence and multiplicity of solutions for generalized Yamabe equations on Riemannian manifolds of the form
\(-\Delta_g w+\alpha(\sigma)w=\lambda K(\sigma) f(w)\) for appropriate values of the real parameter \(\lambda\) and under some growth assumptions on the nonlinearity \(f\). The apporoach relies on the three critical point theorem in the spirit of G. Bonanno and P. Candito [J. Differ. Equations 244, No. 12, 3031–3059 (2008; Zbl 1149.49007)].
Reviewer: Marius Ghergu (Dublin)
MSC:
| 35J60 | Nonlinear elliptic equations |
| 35A01 | Existence problems for PDEs: global existence, local existence, non-existence |
| 58J05 | Elliptic equations on manifolds, general theory |
Keywords:
generalized Yamabe equation; Riemannian manifold; Emden-Fowler problem; existence of solutions; variational methodsCitations:
Zbl 1149.49007References:
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