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 |
| Summary: | <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> |
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| ISSN: | 1687-1839 1687-1847 |