Ambrosetti–Prodi type result of first-order differential equations with locally coercive nonlinearities
In this paper, the authors obtain an Ambrosetti–Prodi type result of T -periodic solutions of the first-order differential equations u ′ ( t ) = a ( t ) u ( t ) - f ( t , u ( t ) ) + s , t ∈ R by topological degree method, where T > 0 is a constant, a : R → [ 0 , ∞ ) are T -periodic functions wit...
Saved in:
| Published in | Monatshefte für Mathematik Vol. 202; no. 2; pp. 377 - 395 |
|---|---|
| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Vienna
Springer Vienna
01.10.2023
Springer Nature B.V |
| Subjects | |
| Online Access | Get full text |
Cover
Loading…
| Summary: | In this paper, the authors obtain an Ambrosetti–Prodi type result of
T
-periodic solutions of the first-order differential equations
u
′
(
t
)
=
a
(
t
)
u
(
t
)
-
f
(
t
,
u
(
t
)
)
+
s
,
t
∈
R
by topological degree method, where
T
>
0
is a constant,
a
:
R
→
[
0
,
∞
)
are
T
-periodic functions with
∫
0
T
a
(
t
)
d
t
=
0
,
s
∈
R
is a parameter;
f
is a Carathéodory function and
T
-periodic for the first variable, which
f
(
t
,
u
) satisfies locally coercive at infinity. |
|---|---|
| ISSN: | 0026-9255 1436-5081 |
| DOI: | 10.1007/s00605-023-01821-6 |