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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 Salón 2 vCal iCal

We consider the stationary Schrödinger equation given by
\label{es}
-\Delta u + Vu = a(x) |u|^{p-2} u, \quad u \in H^1(\mathbb{R}^N),

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.