Title | INFINITELY MANY HOMOCLINIC SOLUTIONS FOR SECOND ORDER DIFFERENCE EQUATIONS WITH p-LAPLACIAN |
Publication Type | Journal Article |
Year of Publication | 2015 |
Authors | Graef, JR, KONG, LINGJU, WANG, MIN |
Volume | 19 |
Issue | 1 |
Start Page | 95 |
Pagination | 8 |
Date Published | 2015 |
ISSN | 1083-2564 |
AMS | 37C20, 39A10, 58E0 |
Abstract | By using critical point theory, the authors study the existence of infinitely many homoclinic solutions to the difference equation $${ −∆a(k)\phi_p(∆u(k − 1)) + b(k)\phi_p(u(k)) = λf(k, u(k))), \ \ k ∈ \mathbb{Z} }$$, where ${p > 1}$ is a real number, ${ \phi_p(t) = |t|^{p−2} t}$ for ${ t ∈ \mathbb{R},\ \ λ > 0}$ is a parameter, ${ a, b : \mathbb{Z} → (0, ∞), }$ and ${ f : \mathbb{Z} × \mathbb{R} → \mathbb{R} }$ is a continuous function in the second variable. Some known work in the literature is extended. |
URL | http://www.acadsol.eu/en/articles/19/1/7.pdf |
Refereed Designation | Refereed |
Full Text | REFERENCES |