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.