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On global well-posedness for a class of nonlocal dispersive wave equations
Multiple solutions for a class of quasilinear problems
| 1. | Departamento de Matemática, IMECC - UNICAMP , Caixa Postal 6065, 13081-970 Campinas-SP, Brazil |
$-\Delta_p u = g(x,u)$ in $\Omega$
$u = 0 $ on $\partial \Omega$,
where $\Omega \subset \mathbb{R}^N$ is an open bounded domain with smooth boundary $\partial \Omega$, $g:\Omega\times\mathbb{R}\to \mathbb{R}$ is a Carathéodory function such that $g(x,0)=0$ and which is asymptotically linear. We suppose that $g(x,t)/t$ tends to an $L^r$-function, $r>N/p$ if 1 < p ≤ N and $r=1$ if $p>N$, which can change sign. We consider both the resonant and the nonresonant cases.
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