A remark on least energy solutions in $\mathbf {R}^N$
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- by Louis Jeanjean and Kazunaga Tanaka
- Proc. Amer. Math. Soc. 131 (2003), 2399-2408
- DOI: https://doi.org/10.1090/S0002-9939-02-06821-1
- Published electronically: November 13, 2002
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Abstract:
We study a mountain pass characterization of least energy solutions of the following nonlinear scalar field equation in $\mathbf {R}^N$: \begin{equation*} -\Delta u = g(u), u \in H^1(\mathbf {R}^N), \end{equation*} where $N\geq 2$. Without the assumption of the monotonicity of $t\mapsto \frac {g(t)}{t}$, we show that the mountain pass value gives the least energy level.References
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Bibliographic Information
- Louis Jeanjean
- Affiliation: Equipe de Mathématiques (UMR CNRS 6623), Université de Franche-Comté, 16 Route de Gray, 25030 Besançon, France
- MR Author ID: 318795
- Email: jeanjean@math.univ-fcomte.fr
- Kazunaga Tanaka
- Affiliation: Department of Mathematics, School of Science and Engineering, Waseda University, 3-4-1 Ohkubo, Skinjuku-ku, Tokyo 169-8555, Japan
- Email: kazunaga@mn.waseda.ac.jp, kazunaga@waseda.jp
- Received by editor(s): March 6, 2002
- Published electronically: November 13, 2002
- Additional Notes: The second author was partially supported by a Waseda University Grant for Special Research Projects 2001A-098.
- Communicated by: David S. Tartakoff
- © Copyright 2002 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 131 (2003), 2399-2408
- MSC (2000): Primary 35J20; Secondary 35J60, 58E05
- DOI: https://doi.org/10.1090/S0002-9939-02-06821-1
- MathSciNet review: 1974637