Infinitely many solutions to fourth order superlinear periodic problems

Conti, Monica; Terracini, Susanna; Verzini, Gianmaria

doi:10.1090/S0002-9947-03-03514-1

Infinitely many solutions to fourth order superlinear periodic problems
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by Monica Conti, Susanna Terracini and Gianmaria Verzini PDF

Trans. Amer. Math. Soc. 356 (2004), 3283-3300 Request permission

Abstract:

We present a new min–max approach to the search of multiple $T$–periodic solutions to a class of fourth order equations \[ u^{iv}(t)-c u''(t)=f(t,u(t)),\hspace {5mm}t\in [0,T],\] where $f(t,u)$ is continuous, $T$–periodic in $t$ and satisfies a superlinearity assumption when $|u|\to \infty$. For every $n\in \mathbb {N}$, we prove the existence of a $T$–periodic solution having exactly $2n$ zeroes in $(0,T]$.

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