| Contents |
| We prove the existence and multiplicity of solutions presenting a
precise nodal behavior for two classes one-dimensional nonlinear
Schr\"{o}dinger equation as
$$ -\varepsilon^2 u'' + V(x) u = f(u)$$
and
$$u'' + k u - a(x) f(u) = 0,$$
for some special forms of the potential $V(x)$ or the coefficient
$a(x).$ The term $f(u)$ generalizes the typical $p$-power
nonlinearity considered by several authors in this context. We
discuss the existence and multiplicity of periodic, Neumann,
homoclinic and heteroclinic solutions. This talk is based on
recent joint works with Chiara Zanini and Elisa Ellero. |
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