The Use of Cerami Sequences in Critical Point Theory
The concept of linking was developed to produce Palais-Smale (PS) sequences G(uk)→a, G'(uk)→0 for C1functionals G that separate linking sets. These sequences produce critical points if they have convergent subsequences (i.e., if G satisfies the PS condition). In the past, we have shown that P...
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| Language: | English |
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Wiley
2007-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2007/58948 |
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| author | Martin Schechter |
| author_facet | Martin Schechter |
| author_sort | Martin Schechter |
| collection | DOAJ |
| description | The concept of linking was developed to produce Palais-Smale (PS) sequences G(uk)→a, G'(uk)→0
for C1functionals G that separate linking sets. These sequences produce critical points if
they have convergent subsequences (i.e., if G satisfies the PS condition). In the past, we have shown that PS sequences can be obtained even when linking does not exist. We now show that such situations produce more useful sequences. They not only produce PS sequences, but also Cerami sequences satisfying G(uk)→a, (1+||uk||)G'(uk)→ 0 as well. A Cerami sequence can produce a critical point even when a PS sequence does not. In this situation, it is no longer necessary to show that
G satisfies the PS condition, but only that it satisfies the easier Cerami condition (i.e., that Cerami sequences have convergent subsequences). We provide examples and applications. We also give generalizations to situations when the separating criterion is violated. |
| format | Article |
| id | doaj-art-342e19309fe24f1fbc950072eeb933ff |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2007-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-342e19309fe24f1fbc950072eeb933ff2025-02-03T00:59:35ZengWileyAbstract and Applied Analysis1085-33751687-04092007-01-01200710.1155/2007/5894858948The Use of Cerami Sequences in Critical Point TheoryMartin Schechter0Department of Mathematics, University of California, Irvine 92697-3875, CA, USAThe concept of linking was developed to produce Palais-Smale (PS) sequences G(uk)→a, G'(uk)→0 for C1functionals G that separate linking sets. These sequences produce critical points if they have convergent subsequences (i.e., if G satisfies the PS condition). In the past, we have shown that PS sequences can be obtained even when linking does not exist. We now show that such situations produce more useful sequences. They not only produce PS sequences, but also Cerami sequences satisfying G(uk)→a, (1+||uk||)G'(uk)→ 0 as well. A Cerami sequence can produce a critical point even when a PS sequence does not. In this situation, it is no longer necessary to show that G satisfies the PS condition, but only that it satisfies the easier Cerami condition (i.e., that Cerami sequences have convergent subsequences). We provide examples and applications. We also give generalizations to situations when the separating criterion is violated.http://dx.doi.org/10.1155/2007/58948 |
| spellingShingle | Martin Schechter The Use of Cerami Sequences in Critical Point Theory Abstract and Applied Analysis |
| title | The Use of Cerami Sequences in Critical Point Theory |
| title_full | The Use of Cerami Sequences in Critical Point Theory |
| title_fullStr | The Use of Cerami Sequences in Critical Point Theory |
| title_full_unstemmed | The Use of Cerami Sequences in Critical Point Theory |
| title_short | The Use of Cerami Sequences in Critical Point Theory |
| title_sort | use of cerami sequences in critical point theory |
| url | http://dx.doi.org/10.1155/2007/58948 |
| work_keys_str_mv | AT martinschechter theuseofceramisequencesincriticalpointtheory AT martinschechter useofceramisequencesincriticalpointtheory |