Electronic Journal of Differential Equations,
Vol. 2009(2009), No. 131, pp. 1-16.
Title: Multiple solutions for nonlinear elliptic equations on
Riemannian manifolds
Authors: Wenjing Chen (Jiangxi Normal Univ., Nanchang, China)
Jianfu Yang (Jiangxi Normal Univ., Nanchang, China)
Abstract:
Let $(\mathcal{M}, g)$ be a compact, connected, orientable,
Riemannian $n$-manifold of class $C^{\infty}$
with Riemannian metric $g$ $(n\geq 3)$. We study the
existence of solutions to the equation
$$
-\varepsilon^2\Delta_{g} u+V(x)u=K(x)|u|^{p-2}u
$$
on this Riemannian manifold. Here $2