Existence and uniqueness of positive even homoclinic solutions for second order differential equations
This paper is concerned with the existence of positive even homoclinic solutions for the p-Laplacian equation (|u 0 p−2u 0 0 − a(t)|u| p−2u + f(t, u) = 0, t ∈ R, where p ≥ 2 and the functions a and f satisfy some reasonable conditions. Using the Mountain Pass Theorem, we obtain the existence of a po...
Elmentve itt :
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| Dokumentumtípus: | Folyóirat |
| Megjelent: |
2019
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| Sorozat: | Electronic journal of qualitative theory of differential equations
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| Kulcsszavak: | Másodrendű differenciálegyenlet |
| doi: | 10.14232/ejqtde.2019.1.45 |
| Online Access: | http://acta.bibl.u-szeged.hu/62123 |
| Tartalmi kivonat: | This paper is concerned with the existence of positive even homoclinic solutions for the p-Laplacian equation (|u 0 p−2u 0 0 − a(t)|u| p−2u + f(t, u) = 0, t ∈ R, where p ≥ 2 and the functions a and f satisfy some reasonable conditions. Using the Mountain Pass Theorem, we obtain the existence of a positive even homoclinic solution. In case p = 2, the solution obtained is unique under a condition of monotonicity on the function u 7−→ f(t,u) u . Some known results in the literature are generalized and significantly improved. |
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| Terjedelem/Fizikai jellemzők: | 1-12 |
| ISSN: | 1417-3875 |