A remark on least energy solutions in $\mathbf {R}^N$
Authors:
Louis Jeanjean and Kazunaga Tanaka
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
Published electronically:
November 13, 2002
MathSciNet review:
1974637
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
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.
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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
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
Keywords:
Nonlinear elliptic equations in $\mathbf {R}^N$,
least energy solutions,
mountain pass theorem
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
Article copyright:
© Copyright 2002
American Mathematical Society
