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k-component disconjugacy for systems of ordinary differential equations

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

Optimality and existence for Lipschitz equations

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.

Solution matching for boundary value problems for linear equations

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

k-component disconjugacy for systems of ordinary differential equations

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

Solution matching for boundary value problems for linear equations

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

Optimality and existence for Lipschitz equations

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.

Continuous dependence and differentiation of solutions of finite difference equations

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

Existence of a positive solution for an nth order boundary value problem for nonlinear difference equations

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

Solvability of a nonlinear second order conjugate eigenvalue problem on a time scale

? 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

Solvability of a nonlinear second order conjugate eigenvalue problem on a time scale

(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

Existence and Nonexistence of Positive Solutions for Coupled Riemann-Liouville Fractional Boundary Value Problems

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

Existence and Nonexistence of Positive Solutions for Coupled Riemann-Liouville Fractional Boundary Value Problems

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

Positive solutions for a system of semipositone coupled fractional boundary value problems

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.

Positive Solutions for Systems of Second-Order Difference Equations

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

Nonexistence of positive solutions for a system of coupled fractional boundary value problems

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.

Positive solutions of discrete Neumann boundary value problems with sign-changing nonlinearities

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...

Existence and multiplicity of positive solutions for a system of fractional boundary value problems

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.

Infinitely many solutions for a boundary value problem with impulsive effects

In this paper we are interested in multiplicity results for a nonlinear Dirichlet boundary value problem subject to perturbations of impulsive terms. The study of the problem is based on the variational methods and critical point theory. Infinitely many solutions follow from a recent variational result.MSC: 34B37, 34B15.

A Dual of the Compression-Expansion Fixed Point Theorems

O'Regan: Department of Mathematics, National University of Ireland , Galway , Ireland 1 Johnny Henderson: Department of Mathematics, Baylor University , Waco, TX 76798 , USA 2 Richard Avery: College of Arts