Geodesic
Existence of solutions to $n$-dimensional pendulum-like equations
Electronic Journal of Differential Equations, Tome 2004 (2004).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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 $c\in I_p$.
Classification : 35J25, 35J65
Keywords: pendulum-like equations, boundary value problems, topological methods 
@article{EJDE_2004__2004__a149,
     author = {Amster, Pablo and De Napoli, Pablo L. and Mariani, Maria Cristina},
     title = {Existence of solutions to $n$-dimensional pendulum-like equations},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2004},
     year = {2004},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2004__2004__a149/}
}
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Amster, Pablo; De Napoli, Pablo L.; Mariani, Maria Cristina. Existence of solutions to $n$-dimensional pendulum-like equations. Electronic Journal of Differential Equations, Tome 2004 (2004). http://geodesic.mathdoc.fr/item/EJDE_2004__2004__a149/