Nonlinear scalar field equations in $\mathbb{R}^{N}$: mountain pass and symmetric mountain pass approaches
Keywords
Nonlinear scalar field equations, radially symmetric solutions, minimax methodsAbstract
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.Downloads
Published
2010-04-23
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1.
HIRATA, Jun, IKOMA, Norihisa and TANAKA, Kazunaga. Nonlinear scalar field equations in $\mathbb{R}^{N}$: mountain pass and symmetric mountain pass approaches. Topological Methods in Nonlinear Analysis. Online. 23 April 2010. Vol. 35, no. 2, pp. 253 - 276. [Accessed 24 April 2024].
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