### Nonlinear scalar field equations in $\mathbb{R}^{N}$: mountain pass and symmetric mountain pass approaches

#### Abstract

We study the existence of radially symmetric solutions of

the following

nonlinear scalar field equations in $\mathbb{R}^N$:

\begin{gather*}

-\Delta u=g(u) \quad \text{in }\mathbb{R}^N,\\

u\in H^1(\mathbb R^N).

\end{gather*}

We give an extension of the existence results due to

H. Berestycki, T. Gallouët and O. Kavian [< i> Equations de Champs scalaires euclidiens

non linéaires dans le plan< /i> , C. R. Acad. Sci. Paris Ser. I Math. < b> 297< /b> , 307–310].< /p>

< p> We take a mountain pass approach in $H^1(\mathbb{R}^N)$ and introduce

a new method generating

a Palais-Smale sequence with an additional property related

to Pohozaev identity.

the following

nonlinear scalar field equations in $\mathbb{R}^N$:

\begin{gather*}

-\Delta u=g(u) \quad \text{in }\mathbb{R}^N,\\

u\in H^1(\mathbb R^N).

\end{gather*}

We give an extension of the existence results due to

H. Berestycki, T. Gallouët and O. Kavian [< i> Equations de Champs scalaires euclidiens

non linéaires dans le plan< /i> , C. R. Acad. Sci. Paris Ser. I Math. < b> 297< /b> , 307–310].< /p>

< p> We take a mountain pass approach in $H^1(\mathbb{R}^N)$ and introduce

a new method generating

a Palais-Smale sequence with an additional property related

to Pohozaev identity.

#### Keywords

Nonlinear scalar field equations; radially symmetric solutions; minimax methods

#### Full Text:

FULL TEXT### Refbacks

- There are currently no refbacks.