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arxiv: 1004.2775 · v1 · submitted 2010-04-16 · 🧮 math.AP

Existence of ground states for fourth-order wave equations

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keywords existencefourth-ordergroundwavedeltaequationequationsfocusing
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Focusing on the fourth-order wave equation $u_{tt} + \Delta^2 u + f(u)= 0$, we prove the existence of ground state solutions $u=u(x+ct)$ for an optimal range of speeds $c\in\mathbb{R}^n$ and a variety of nonlinearities $f$.

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