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A remark on least energy solutions in $\mathbf{R}^N$

Author(s): Louis Jeanjean; Kazunaga Tanaka
Journal: Proc. Amer. Math. Soc. 131 (2003), 2399-2408.
MSC (2000): Primary 35J20; Secondary 35J60, 58E05
Posted: 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{displaymath}-\Delta u = g(u),\, u \in H^1(\mathbf{R}^N), \end{displaymath}

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.

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Additional Information:

Louis Jeanjean
Affiliation: Equipe de Mathématiques (UMR CNRS 6623), Université de Franche-Comté, 16 Route de Gray, 25030 Besançon, France
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

DOI: 10.1090/S0002-9939-02-06821-1
PII: S 0002-9939(02)06821-1
Keywords: Nonlinear elliptic equations in $\mathbf{R}^N$, least energy solutions, mountain pass theorem
Received by editor(s): March 6, 2002
Posted: 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 of article: Copyright 2002, American Mathematical Society

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