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Ground state for a stationary Schrödinger equation with several limit problems

Ponente: Julián Chagoya
Institución: IM-UNAM
 Tipo de Evento: Investigación
Cuándo 31/03/2016
de 10:00 a 11:00
Dónde Salón 2
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We consider the stationary Schrödinger equation given by
\begin{equation} \label{es}
-\Delta u + Vu = a(x) |u|^{p-2} u, \quad u \in H^1(\mathbb{R}^N),
\end{equation}
where \(2 <p <2^*\)  (\(2^*=2N/(N-2)\) for \(N \geq 3\) , \(2^*=\infty\) for \(N=2\))  and \(a,V \in L^\infty(\mathbb{R}^N)\), \(\inf V >0\). We prove the existence of a ground state in the case where \(a\) is sign-changing and the limits \(\lim_{\|x\| \to \infty} a(x)\),\(\lim_{\|x\| \to \infty} V(x)\) do not exist. To obtain this result we have developed a variation of the Splitting Lemma in which several limit problems are considered.