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Wednesday October 25, 2017 (2 pm, Aula C)

Elisandra Gloss

(Universidade Federal da Paraíba)

On a class of quasilinear Schrödinger equations

with superlinear or asymptotically linear terms

(Universidade Federal da Paraíba)

On a class of quasilinear Schrödinger equations

with superlinear or asymptotically linear terms

Abstract:
We will talk about existence and nonexistence of nonzero solutions for
the following class of quasilinear Schrödinger equations:

`-\Delta u+V(x)u+
\frac{\kappa}{2}[\Delta(u^{2})]u=h(u), \quad x \in
\mathbb{R}^N,`

where `\kappa` is a real parameter, `N\geq3`,
`V(x)` and `h(t)` are continuous
functions satisfying additional conditions. In order to prove our
existence result we use minimax techniques together with careful
`L^{\infty}-`estimates. Moreover, we show a Pohozaev identity which
justifies that `2^\ast=2N``/``(N-2)` is the critical exponent
for this class of problems when `\kappa` is positive, in contrast to
`22^\ast=4N``/``(N-2)` for `\kappa` negative and it is also used to
show nonexistence results.