MR2427544
Baoqiang YAN, Donal O'REGAN and Ravi P. AGARWAL
Baoqiang YAN, Donal O'REGAN and Ravi P. AGARWAL
Unbounded Positive Solutions for Second Order Singular Boundary Value Problems with Derivative Dependence on Infinite Intervals
Funkcialaj Ekvacioj. Serio Internacia
51
2008
81--106
http://fe.math.kobe-u.ac.jp/FE/FullPapers/51-1/51_81.pdf
http://www.ams.org/mathscinet-getitem?mr=MR2427544
The existence of at least one unbounded positive solution and the existence of multiple unbounded positive solutions are established for the singular second-order boundary value problem $p(t)^{-1}(p(t)x'(t))'+\Phi(t)f(t,x,px')=0$, $0<t<+\infty$, $x(0)=0$, $\lim_{t\to+\infty}p(t)x'(t)=0$, using the fixed point index, where $f$ may be singular at $px'=0$.
Boundary value problems, Singularity, Fixed point index.
34B16, 34B18.
51-81
2008
Unbounded Positive Solutions for Second Order Singular Boundary Value Problems with Derivative Dependence on Infinite Intervals
Baoqiang YAN, Donal O'REGAN and Ravi P. AGARWAL
Baoqiang YAN, Donal O'REGAN and Ravi P. AGARWAL
1
Agarwal, R. P.; O'Regan, D.
Singular problems on the infinite interval modelling phenomena in draining flows
IMA J. Appl. Math.
66
2001
621-635
MR1869408
2
Agarwal, R. P.; O'Regan, D.
Boundary value problems on the half line in the theory of colloids
Math. Prob. Eng.
8
2002
143-150
MR1918316
3
Agarwal, R. P.; O'Regan, D.
Existence theory for single and multiple solutions to singular positone boundary value problems
J. Differential Equations
175
2001
393-414
MR1855974
4
Agarwal, R. P.; O'Regan, D.
Twin solutions to singular Dirichlet problems
J. Math. Anal. Appl.
240
1999
433-445
MR1731655
5
Baxley, J. V.
Existence and uniqueness for nonlinear boundary value problems on infinite intervals
J. Math. Anal. Appl.
147
1990
122-133
MR1044690
6
Bobisud, L. E.
Existence of Positive solutions to some nonlinear singular boundary value problems on finite and infinite intervals
J. Math. Anal. Appl.
173
1993
69-83
MR1205910
7
Chapman, S. J.
Superheating field of type II superconductors
SIAM J. Appl. Math.
55
1995
1233-1258
MR1349308
8
Chen, S.; Zhang, Y.
Singular boundary value problems on a half-line
J. Math. Anal. Appl.
195
1995
449-468
MR1354555
9
Corduneanu, C.
Integral equations and stability of feedback systems
Academic Press, New York
1973
MR0358245
10
Guo, D.
Multiple positive solutions for $n$th-order impulsive integro-differential equations in Banach spaces
Nonlinear Anal.
60
2005
955-976
MR2113166
11
Guo, D.
Multiple positive solutions for a class of nonlinear integro-differential equations in Banach spaces
Appl. Math. Comput.
154
2004
469-485
MR2111384
12
Guo, D.
Multiple positive solutions of a boundary value problem for $n$th-order impulsive integro-differential equations in a Banach space
Nonlinear Anal.
56
2004
985-1006
MR2038733
13
Guo, D.; Lakshmikantham, V.
Nonlinear problems in abstract cones
Academic Press, Inc., New York
1988
MR0959889
14
Henderson, J.; Thompson, H. B.
Multiple symmetric positive solutions for a second order boundary value problem
Proc. Amer. Math. Soc.
128
2000
2373-2379
MR1709753
15
O'Regan, D.
Existence theory for nonlinear ordinary differential equations
Kluwer, Dordrecht
1997
MR1449397
16
O'Regan, D.
Theory of singular boundary value problems
World Scientific, Singapore
1994
MR1286741
17
Palamides, P. K.; Galanis, G. N.
Positive, unbounded and monotone solutions of the singular second Painleve equation on the half-line
Nonlinear Anal.
57
2004
401-419
MR2064098
18
Yang, G. C.
Second order singular boundary value problems with sign-changing nonlinearities on infinite intervals
Nonlinear Anal. Forum
9
2004
169-174
MR2112006
19
Yermachenko, I.; Sadyrbaev, F.
Quasilinearization and multiple solutions of the Emden-Fowler type equation
Math. Model. Anal.
10
2005
41-50
MR2129748