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Infinitely many solutions to fourth order superlinear periodic problems
Authors:Monica Conti  Susanna Terracini  Gianmaria Verzini
Institution:Dipartimento di Matematica del Politecnico, piazza Leonardo da Vinci, 32 - 20133 Milano (I), Italy ; Dipartimento di Matematica e Applicazioni, Università di Milano Bicocca, Via Bicocca degli Arcimboldi 8, 20126 Milano (I), Italy ; Dipartimento di Matematica del Politecnico, piazza Leonardo da Vinci, 32 - 20133 Milano (I), Italy
Abstract:We present a new min-max approach to the search of multiple $T$-periodic solutions to a class of fourth order equations

\begin{displaymath}u^{iv}(t)-c u'(t)=f(t,u(t)),\hspace{5mm}t\in0,T],\end{displaymath}

where $f(t,u)$ is continuous, $T$-periodic in $t$ and satisfies a superlinearity assumption when $\vert u\vert\to\infty$. For every $n\in\mathbb{N}$, we prove the existence of a $T$-periodic solution having exactly $2n$ zeroes in $(0,T]$.

Keywords:Oscillating solutions  fourth order equations  boundary value problems  variational methods
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