Electronic Journal of Differential Equations,
Vol. 2004(2004), No. 125, pp. 1-8.

Title: Existence of solutions to n-dimensional pendulum-like equations

Authors: Pablo Amster  (Univ. de Buenos Aires, Argentina)
         Pablo L. De Napoli (Univ. de Buenos Aires, Argentina)
	 Maria Cristina Mariani (New Mexico State Univ., NM, USA)

Abstract: 
 We study the elliptic boundary-value problem
 $$\displaylines{
 \Delta u + g(x,u)  = p(x) \quad \hbox{in } \Omega \cr
 u\big|_{\partial \Omega}  = \hbox{\rm constant}, \quad
 \int_{\partial\Omega} \frac {\partial u}{\partial \nu} = 0, 
 }$$
 where $g$ is $T$-periodic in $u$, 
 and $\Omega \subset \mathbb{R}^n$ is a bounded domain.
 We prove the existence of a solution under a condition on
 the average of the forcing term $p$.
 Also, we prove the existence of a compact interval 
 $I_p \subset \mathbb{R}$ such that the problem is solvable 
 for $\tilde p(x) = p(x) + c$ if and only if
 $c\in I_p$. 
 
Submitted June 3, 2004. Published October 20, 2004.
Math Subject Classifications: 35J25, 35J65.
Key Words: Pendulum-like equations; boundary value problems; 
           topological methods.