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Internat. J. Math. & Math. Sci.
Vol.
**JOHNNY** **HENDERSON** 0
0 Department of Mathematics Auburn Unlverslty Auburn , Alabama 36849 , USA
BSTKACT: DisconJugacy of the kth component of the ruth order

Solutions of certain boundary value problems are shown to exist for the nth order differential equation y(n)=f(t,y,y′,…,y(n−1)), where f is continuous on a slab (a,b)×Rn and f satisfies a Lipschitz condition on the slab. Optimal length subintervals of (a,b) are determined, in terms of the Lipschitz coefficients, on which there exist unique solutions.

Internat. J. Math. & Math. Sci.
VOL.
**JOHNNY** **HENDERSON** DeparUeent o Algebra 0
Comblnatorics 0
Analysis 0
0 Auburn University Auburn , Alabama 36849 U.S.A
For the linear differential equation, y(n

Internat. J. Math. & Math. Sci.
Vol.
**JOHNNY** **HENDERSON** 0
0 Department of Mathematics Auburn Unlverslty Auburn , Alabama 36849 , USA
BSTKACT: DisconJugacy of the kth component of the ruth order

Internat. J. Math. & Math. Sci.
VOL.
**JOHNNY** **HENDERSON** DeparUeent o Algebra 0
Comblnatorics 0
Analysis 0
0 Auburn University Auburn , Alabama 36849 U.S.A
For the linear differential equation, y(n

Solutions of certain boundary value problems are shown to exist for the nth order differential equation y(n)=f(t,y,y′,…,y(n−1)), where f is continuous on a slab (a,b)×Rn and f satisfies a Lipschitz condition on the slab. Optimal length subintervals of (a,b) are determined, in terms of the Lipschitz coefficients, on which there exist unique solutions.

Internat. J. Math. & Math. Sci.
VOL.
CONTINUOUS DEPENDENCE AND DIFFERENTIATION OF SOLUTIONS OF FINITE DIFFERENCE EUQATIONS
**JOHNNY** **HENDERSON** 0
LINDA LEE Department of Algebra 0
Combinatorics 0

Journal of
**JOHNNY** **HENDERSON** AND SUSAN D. LAUER
The nth order eigenvalue problem: ? nx(t) = (?1)n?k?f (t, x(t)), t ? [0, T ], x(0) = x(1) = ? ? ? = x(k ? 1) = x(T + k + 1) = ? ? ? = x(T + n) = 0 ... yields a fixed point of H belonging to P ? (? ? 2\? 1).
this fixed point is a solution of (
1
), (
2
) corresponding to the given ?.
**Johnny** **Henderson** Department of Mathematics Auburn University Auburn

Solutions are obtained of boundary value problems for Lny

Upper and lower solutions are used in establlsning global existence results for certain two–point boundary value problems for y‴=f(x,y,y′,y″) and y(n)=f(x,y,y′,...,y(n−1)).

? with y = H2, then we have
(2.27)
(2.28)
Thus, T y ? y . So, if we define
An application of Theorem 1.9 yields the conclusion of our theorem.
**Johnny** **Henderson**: Department of Mathematics, Auburn

(x) ≤ f (H2) for
0 < x ≤ H2. If y ∈ with y = H2, then we have
(2.27)
(2.28)
Thus, T y ≤ y . So, if we define
An application of Theorem 1.9 yields the conclusion of our theorem.
**Johnny** **Henderson**

University, 700050 Iasi, Romania
Received 12 January 2016; Revised 13 April 2016; Accepted 14 June 2016
Academic Editor: Josef Diblík
Copyright © 2016 **Johnny** **Henderson** et al. This is an open access article

University, 700050 Iasi, Romania
Received 12 January 2016; Revised 13 April 2016; Accepted 14 June 2016
Academic Editor: Josef Diblík
Copyright © 2016 **Johnny** **Henderson** et al. This is an open access article

We study the existence of positive solutions for a system of nonlinear Riemann-Liouville fractional differential equations with sign-changing nonlinearities, subject to coupled integral boundary conditions. MSC: 34A08, 45G15.

Mathematics, Gheorghe Asachi Technical University, 700506 Iasi, Romania
Received 17 March 2015; Accepted 30 August 2015
Academic Editor: Miguel Ángel López
Copyright © 2015 **Johnny** **Henderson** and Rodica Luca

Mathematics, Gheorghe Asachi Technical University, 700506 Iasi, Romania
Received 17 March 2015; Accepted 30 August 2015
Academic Editor: Miguel Ángel López
Copyright © 2015 **Johnny** **Henderson** and Rodica Luca

We investigate the nonexistence of positive solutions for a system of nonlinear Riemann-Liouville fractional differential equations with coupled integral boundary conditions. MSC: 34A08, 45G15.

Our concern is the existence of positive solutions of the discrete Neumann boundary value problem { − Δ 2 u ( t − 1 ) = f ( t , u ( t ) ) , t ∈ [ 1 , T ] Z , Δ u ( 0 ) = Δ u ( T ) = 0 , where f : [ 1 , T ] Z × R + → R is a sign-changing function. By using the Guo-Krasnosel’skiĭ fixed point theorem, the existence and multiplicity of positive solutions are established. The...

We study the existence and multiplicity of positive solutions for a system of nonlinear Riemann-Liouville fractional differential equations, subject to integral boundary conditions. The nonsingular and singular cases for the nonlinearities are investigated.MSC: 34A08, 45G15.