1. CMB 2015 (vol 58 pp. 723)
 Castro, Alfonso; Fischer, Emily

Infinitely Many Rotationally Symmetric Solutions to a Class of Semilinear LaplaceBeltrami Equations on Spheres
We show that a class of semilinear LaplaceBeltrami equations
on the unit sphere
in $\mathbb{R}^n$ has infinitely many rotationally symmetric solutions.
The solutions to
these equations are the solutions to a two point boundary value
problem for a
singular ordinary differential equation. We prove the existence
of such solutions
using energy and phase plane analysis. We derive a
Pohozaevtype
identity
in
order to prove that the energy to an associated initial value
problem tends
to infinity as the energy at the singularity tends to infinity.
The nonlinearity is allowed to grow as fast as $s^{p1}s$ for
$s$ large
with $1 \lt p \lt (n+5)/(n3)$.
Keywords:LaplaceBeltrami operator, semilinear equation, rotational solution, superlinear nonlinearity, subsuper critical nonlinearity Categories:58J05, 35A24 

2. CMB 2010 (vol 53 pp. 674)
 Kristály, Alexandru; Papageorgiou, Nikolaos S.; Varga, Csaba

Multiple Solutions for a Class of Neumann Elliptic Problems on Compact Riemannian Manifolds with Boundary
We study a semilinear elliptic problem on a compact Riemannian
manifold with boundary, subject to an inhomogeneous Neumann
boundary condition. Under various hypotheses on the nonlinear
terms, depending on their behaviour in the origin and infinity, we
prove multiplicity of solutions by using variational arguments.
Keywords:Riemannian manifold with boundary, Neumann problem, sublinearity at infinity, multiple solutions Categories:58J05, 35P30 

3. CMB 2008 (vol 51 pp. 467)
 Wang, Yue

Coupled Vortex Equations on Complete KÃ¤hler Manifolds
In this paper, we first investigate the Dirichlet
problem for coupled vortex equations. Secondly, we give existence
results for solutions of the coupled vortex equations on a class
of complete noncompact K\"ahler manifolds which include
simplyconnected strictly negative curved manifolds, Hermitian
symmetric spaces of noncompact type and strictly pseudoconvex
domains equipped with the Bergmann metric.
Categories:58J05, 53C07 
