Positive solutions for Neumann boundary value problems of nonlinear second-order integro-differential equations in ordered Banach spaces
The paper deals with the existence of positive solutions for Neumann boundary value problems of nonlinear second-order integro-differential equations - u ″ ( t ) + M u ( t ) = f ( t , u ( t ) , ( S u ) ( t ) ) , 0 < t < 1 , u ′ ( 0 ) = u ′ ( 1 ) = θ and u ″ ( t ) + M u ( t ) = f ( t , u ( t )...
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| Published in: | Journal of inequalities and applications Vol. 2011; no. 1; pp. 1 - 11 |
|---|---|
| Main Authors: | , |
| Format: | Journal Article |
| Language: | English |
| Published: |
Cham
Springer International Publishing
30.09.2011
Springer Nature B.V SpringerOpen |
| Subjects: | |
| ISSN: | 1029-242X, 1025-5834, 1029-242X |
| Online Access: | Get full text |
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| Summary: | The paper deals with the existence of positive solutions for Neumann boundary value problems of nonlinear second-order integro-differential equations
-
u
″
(
t
)
+
M
u
(
t
)
=
f
(
t
,
u
(
t
)
,
(
S
u
)
(
t
)
)
,
0
<
t
<
1
,
u
′
(
0
)
=
u
′
(
1
)
=
θ
and
u
″
(
t
)
+
M
u
(
t
)
=
f
(
t
,
u
(
t
)
,
(
S
u
)
(
t
)
)
,
0
<
t
<
1
,
u
′
(
0
)
=
u
′
(
1
)
=
θ
in an ordered Banach space
E
with positive cone
K
, where
M >
0 is a constant,
f
: [0, 1] ×
K
×
K
→
K
is continuous,
S
:
C
([0, 1],
K
) →
C
([0, 1],
K
) is a Fredholm integral operator with positive kernel. Under more general order conditions and measure of noncompactness conditions on the nonlinear term
f
, criteria on existence of positive solutions are obtained. The argument is based on the fixed point index theory of condensing mapping in cones.
Mathematics Subject Classification (2000):
34B15; 34G20. |
|---|---|
| Bibliography: | SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 14 ObjectType-Article-2 content type line 23 |
| ISSN: | 1029-242X 1025-5834 1029-242X |
| DOI: | 10.1186/1029-242X-2011-73 |