Existence of positive periodic solutions for Liénard equations with an indefinite singularity of attractive type
In this paper, we study the periodic problem for the Liénard equation with an indefinite singularity of attractive type x ″ + f ( x ) x ′ + φ ( t ) x + r ( t ) x μ = 0 , where f : ( 0 , + ∞ ) → R is continuous and may have singularities at zero, r , φ : R → R are T -periodic functions, and μ is a po...
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Published in | Boundary value problems Vol. 2018; no. 1; pp. 1 - 19 |
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Main Authors | , |
Format | Journal Article |
Language | English |
Published |
Cham
Springer International Publishing
28.06.2018
Hindawi Limited SpringerOpen |
Subjects | |
Online Access | Get full text |
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Summary: | In this paper, we study the periodic problem for the Liénard equation with an indefinite singularity of attractive type
x
″
+
f
(
x
)
x
′
+
φ
(
t
)
x
+
r
(
t
)
x
μ
=
0
,
where
f
:
(
0
,
+
∞
)
→
R
is continuous and may have singularities at zero,
r
,
φ
:
R
→
R
are
T
-periodic functions, and
μ
is a positive constant. Using the method of upper and lower functions, we obtain some new results on the existence of positive periodic solutions to the equation. |
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ISSN: | 1687-2770 1687-2762 1687-2770 |
DOI: | 10.1186/s13661-018-1020-0 |