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# Ground state for a stationary Schrödinger equation with several limit problems

Ponente: Julián Chagoya
Institución: IM-UNAM
Cuándo 11/12/2014 de 12:00 a 13:30 Salón de seminarios Graciela Salicrup vCal iCal

We consider the stationary Schrödinger equation given by
\label{es}
-\Delta u + u = 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 $$a \in L^\infty(\mathbb{R}^N)$$. We
search for ground states for this equation using the Concentration
Compactness Principle. We are interested in cases where $$a$$ is
sign-changing and $$\lim_{\|x\| \to \infty} a(x)$$ doesn't exist,
so we will have to consider various limit problems for the
Concentration Compactness Principle. We will present some particular
cases and from them extract a set of more general hypothesis that
assure the existence of a ground state.