Change search

Cite
Citation style
• apa
• ieee
• modern-language-association-8th-edition
• vancouver
• Other style
More styles
Language
• de-DE
• en-GB
• en-US
• fi-FI
• nn-NO
• nn-NB
• sv-SE
• Other locale
More languages
Output format
• html
• text
• asciidoc
• rtf
Multibump solutions and critical groups
Dipartimento di Matematica, Politecnico di Milano, Milano, Italy.
Stockholm University, Faculty of Science, Department of Mathematics. matematik.
Department of Mathematical Sciences, Tsinghua University, Beijing, China.
2009 (English)In: Transactions of the American Mathematical Society, ISSN 0002-9947, E-ISSN 1088-6850, Vol. 361, no 6, p. 33p. 3159-3187Article in journal (Refereed) Published
##### Abstract [en]

We consider the Newtonian system $-\ddot q+B(t)q = W_q(q,t)$ with $B$, $W$ periodic in $t$, $B$ positive definite, and show that for each isolated homoclinic solution $q_0$ having a nontrivial critical group (in the sense of Morse theory) multibump solutions (with $2\le k\le\iy$ bumps) can be constructed by gluing translates of $q_0$. Further we show that the collection of multibumps is semiconjugate to the Bernoulli shift. Next we consider the Schr\"odinger equation $-\Delta u+V(x)u = g(x,u)$ in $\RN$, where $V$, $g$ are periodic in $x_1,\ldots,x_N$, $\sigma(-\Delta+V)\subset (0,\iy)$, and we show that similar results hold in this case as well. In particular, if $g(x,u)=|u|^{2^*-2}u$, $N\ge 4$ and $V$ changes sign, then there exists a solution minimizing the associated functional on the Nehari manifold. This solution gives rise to multibumps if it is isolated.

##### Place, publisher, year, edition, pages
Providence, R.I.: American Mathematical Society , 2009. Vol. 361, no 6, p. 33p. 3159-3187
##### Keyword [en]
Multibump solution, critical group, Bernoulli shift, Newtonian system, Schrödinger equation, critical exponent
##### National Category
Mathematical Analysis
Mathematics
##### Identifiers
ISI: 000264881500014OAI: oai:DiVA.org:su-20661DiVA, id: diva2:187187
Available from: 2007-11-28 Created: 2007-11-28 Last updated: 2017-12-13Bibliographically approved

#### Open Access in DiVA

No full text in DiVA

Publisher's full texthttp://www.ams.org/tran/2009-361-06/S0002-9947-09-04669-8/S0002-9947-09-04669-8.pdf

#### Search in DiVA

Szulkin, Andrzej
##### By organisation
Department of Mathematics
##### In the same journal
Transactions of the American Mathematical Society
##### On the subject
Mathematical Analysis

doi
urn-nbn

#### Altmetric score

doi
urn-nbn
Total: 55 hits

Cite
Citation style
• apa
• ieee
• modern-language-association-8th-edition
• vancouver
• Other style
More styles
Language
• de-DE
• en-GB
• en-US
• fi-FI
• nn-NO
• nn-NB
• sv-SE
• Other locale
More languages
Output format
• html
• text
• asciidoc
• rtf