Existence of Homoclinic Solutions for a Class of Nonlinear Difference Equations
<p/> <p>By using the critical point theory, we establish some existence criteria to guarantee that the nonlinear difference equation <inline-formula><graphic file="1687-1847-2010-470375-i1.gif"/></inline-formula> has at least one homoclinic solution, where <...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2010-01-01
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| Series: | Advances in Difference Equations |
| Online Access: | http://www.advancesindifferenceequations.com/content/2010/470375 |
| _version_ | 1828393185031749632 |
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| author | Chen Peng Tang XH |
| author_facet | Chen Peng Tang XH |
| author_sort | Chen Peng |
| collection | DOAJ |
| description | <p/> <p>By using the critical point theory, we establish some existence criteria to guarantee that the nonlinear difference equation <inline-formula><graphic file="1687-1847-2010-470375-i1.gif"/></inline-formula> has at least one homoclinic solution, where <inline-formula><graphic file="1687-1847-2010-470375-i2.gif"/></inline-formula>, <inline-formula><graphic file="1687-1847-2010-470375-i3.gif"/></inline-formula> and <inline-formula><graphic file="1687-1847-2010-470375-i4.gif"/></inline-formula> is non periodic in <inline-formula><graphic file="1687-1847-2010-470375-i5.gif"/></inline-formula>. Our conditions on the nonlinear term <inline-formula><graphic file="1687-1847-2010-470375-i6.gif"/></inline-formula> are rather relaxed, and we generalize some existing results in the literature.</p> |
| first_indexed | 2024-12-10T07:34:38Z |
| format | Article |
| id | doaj.art-f9ed64128e6e40df9fcbe7c5856c9863 |
| institution | Directory Open Access Journal |
| issn | 1687-1839 1687-1847 |
| language | English |
| last_indexed | 2024-12-10T07:34:38Z |
| publishDate | 2010-01-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Advances in Difference Equations |
| spelling | doaj.art-f9ed64128e6e40df9fcbe7c5856c98632022-12-22T01:57:28ZengSpringerOpenAdvances in Difference Equations1687-18391687-18472010-01-0120101470375Existence of Homoclinic Solutions for a Class of Nonlinear Difference EquationsChen PengTang XH<p/> <p>By using the critical point theory, we establish some existence criteria to guarantee that the nonlinear difference equation <inline-formula><graphic file="1687-1847-2010-470375-i1.gif"/></inline-formula> has at least one homoclinic solution, where <inline-formula><graphic file="1687-1847-2010-470375-i2.gif"/></inline-formula>, <inline-formula><graphic file="1687-1847-2010-470375-i3.gif"/></inline-formula> and <inline-formula><graphic file="1687-1847-2010-470375-i4.gif"/></inline-formula> is non periodic in <inline-formula><graphic file="1687-1847-2010-470375-i5.gif"/></inline-formula>. Our conditions on the nonlinear term <inline-formula><graphic file="1687-1847-2010-470375-i6.gif"/></inline-formula> are rather relaxed, and we generalize some existing results in the literature.</p>http://www.advancesindifferenceequations.com/content/2010/470375 |
| spellingShingle | Chen Peng Tang XH Existence of Homoclinic Solutions for a Class of Nonlinear Difference Equations Advances in Difference Equations |
| title | Existence of Homoclinic Solutions for a Class of Nonlinear Difference Equations |
| title_full | Existence of Homoclinic Solutions for a Class of Nonlinear Difference Equations |
| title_fullStr | Existence of Homoclinic Solutions for a Class of Nonlinear Difference Equations |
| title_full_unstemmed | Existence of Homoclinic Solutions for a Class of Nonlinear Difference Equations |
| title_short | Existence of Homoclinic Solutions for a Class of Nonlinear Difference Equations |
| title_sort | existence of homoclinic solutions for a class of nonlinear difference equations |
| url | http://www.advancesindifferenceequations.com/content/2010/470375 |
| work_keys_str_mv | AT chenpeng existenceofhomoclinicsolutionsforaclassofnonlineardifferenceequations AT tangxh existenceofhomoclinicsolutionsforaclassofnonlineardifferenceequations |