... pages
doi:10.1155/2009/685040
Research Article
Existence of Positive Solution to Second-Order
Three-Point BVPs on Time Scales
Jian-Ping Sun
Department of Applied Mathematics, Lanzhou University of Technology, ... problems on time scales,” Journal of Difference
Equations and Applications, vol. 8, no. 8, pp. 673–688, 2002.
7 E. R. Kaufmann, Positive solutions...
... for the existence of periodic solutions of this
class of nonautonomous scalar dynamic equations on time scales, the approach that authors
used in this paper is based on Mawhin’s continuation theorem.
In ... books.
But the research of periodic solutions on time scales has not got much attention, see
12–16. The methods usually used to explore the existence of perio...
... purpose is to establish sufficient
conditions on the existence of positive solutions to 1.1 by using some fixed point theorems
and some properties of the Green function. By a positive solution to 1.1 ... problem of nonlinear fractional differential
equation,” Electronic Journal of Qualitative Theory of Differential Equations, no. 24, 10 pages, 2008.
9 Z. Bai, On p...
... a<b. Some existence criteria of solution and positive solution are
established by using the Leray-Schauder fixed point theorem.
In this paper, we consider the existence of positive solutions for ... Difference Equations
17 J. Henderson, A. Peterson, and C. C. Tisdell, On the existence and uniqueness of solutions to
boundary value problems on time scales,” Advance...
... belongs to P and φ00. The fractional derivative is
understood here in the Caputo sense.
The aim of our paper is to study the solvability of 1.1 and present the existence of
mild solution of ... Corporation
Advances in Difference Equations
Volume 2011, Article ID 963463, 15 pages
doi:10.1155/2011/963463
Research Article
Existence of Mild Solutions to
Fractional...
... depiction of critical groups. To conquer this difficulty, we compute the Brouwer degree
of the s ets of positive solutions and negative solutions to 1.1. Finally, the third nontrivial
solution to ... is a solution to 3.8,thenu is positive. Since this
contradicts V
∞ ∈ λ
k
,λ
k1
,weconcludethatw ≡ 0 is the only solution to 3.8.A
contradiction to w 1....
... H2,wehavethatF : Y
→ Y
is
continuous. It is easy to see that u ∈ C
2
0, 1 ∩ C
4
0, 1 being a positive solution of BVP1.2
is equivalent to u ∈ Y
being a nonzero solution equation as follows:
u ... positive solutions for nonlocal boundary value problems of fourth order,”
Nonlinear Analysis. Theory, Methods & Applications, vol. 68, no. 3, pp. 645–651, 2008.
9...
... Publishing Corporation
Boundary Value Problems
Volume 2010, Article ID 458015, 16 pages
doi:10.1155/2010/458015
Research Article
Existence of Positive Solutions of
a Singular Nonlinear Boundary ... to check that, for 0 <δ<
δ, all of the conditions
of Theorem A are satisfied. So there exists a connected component C
n
of solutions of 2.30
containing a
n
,b
n
...
... Publishing Corporation
Boundary Value Problems
Volume 2010, Article ID 626054, 18 pages
doi:10.1155/2010/626054
Research Article
Existence of Positive Solutions of
Nonlinear Second-Order Periodic ... the existence of positive solutions of 3.17 will not
be guaranteed in this case.
Proof of Theorem 3.2. We only prove i. ii can be proved by a similar method.
To...
... least one
positive solution.
Proof. Since f
0
∞, similar to the second part of Theorem 3.1, we have Au≥u for
u ∈ P ∩ ∂Ω
H
3
.
By f
∞
∈ 0,ϕ
p
A
1
, similar to the second part of proof of ... K
M
x
for some positive constants K
m
,K
M
. They established the existence results for at least one
positive solution by using a fixed point theorem of cone expansion and...