| Abstract: |
| We are interested in following quasilinear elliptic problem:
\begin{equation*}
-\mathrm{div} \left\{ \phi \left(\frac{u^2+|\nabla u|^2 }{2}\right) \nabla u\right\}
+\phi \left(\frac{u^2+|\nabla u|^2 }{2}\right)u = g(u) \ \hbox{in} \ \mathbb{R}^N,
\end{equation*}
which appears in nonlinear optics. By using the mountain pass theorem together with a technique of adding one dimension of space and the theory of monotone operator, we prove the existence of a non-trivial weak solution
for general nonlinear terms of Berestycki-Lions` type. |
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