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Usted está aquí: Inicio / Actividades / Seminarios / Seminario de Análisis y Ecuaciones Diferenciales / Actividades del Seminario de Análisis y Ecuaciones Diferenciales / Existence and nonexistence results for a class of asymptotically linear non-autonomous equations in \(\mathbb{R}^N\)

Existence and nonexistence results for a class of asymptotically linear non-autonomous equations in \(\mathbb{R}^N\)

Liliane A. Maia (Universidad de Brasilia)- Jueves 4 de abril de 2013, 11:00 hrs.
Ponente:
Cuándo 04/04/2013
de 12:00 a 13:00
Dónde Graciela Salicrup
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We will present some recent results on the existence of solutions for a class of elliptic equations which are asymptotically linear at infinity\[ -\Delta u + V(x) u = a(x) f(u) \quad\in \mathbb{R}^n,\]  where \( 0 < V(x)\to V_\infty\)   and \(0 < a(x)\to a_\infty\),  as  \(|x|\to\infty, V_\infty  < a_\infty\)  and \( f(s)/s \to 1\) as \(s \to \infty\). Using  concentration compactness arguments and a general Pohozaev type manifold, we find bound state solutions via a linking theorem.

Moreover, we show that a minimizing problem, related to the existence of a ground state, has no solution.
This is a work in collaboration with Raquel Lehrer from Universidade Estadual do Oeste do Paraná- UNIOESTE, Campus Cascavel.