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An application of an avery type fixed point theorem to a second order antiperiodic boundary value problem
1.  Department of Mathematics, Nova Southeastern University, 3301 College Avenue, Fort Lauderdale, FL 33314, United States 
References:
[1] 
A. A. Altwaty and P. W. Eloe, The role of concavity in applications of Avery type fixed point theorems to higher order differential equations,, J. Math Inequal., 6 (2012), 79. 
[2] 
A. A. Altwaty and P. W. Eloe, Concavity of solutions of a $2n$th order problem with symmetry,, Opuscula Math., 33 (2013), 603. 
[3] 
D. R. Anderson and R. I. Avery, Fixed point theorem of cone expansion and compression of functional type,, J. Difference Equ. Appl., 8 (2002), 1073. 
[4] 
D. R. Anderson, R. I. Avery and J. Henderson, Functional expansioncompression fixed point theorem of LeggettWilliams type,, Electron. J. Differential Equations, 2010 (): 1. 
[5] 
D. R. Anderson, R. I. Avery, J. Henderson and X. Liu, Operator type expansioncompression fixed point theorem,, Electron. J. Differential Equations, 2011 (): 1. 
[6] 
D. R. Anderson, R. I. Avery, J. Henderson and X. Liu, Fixed point theorem utilizing operators and functionals,, Electron. J. Qual. Theory Differ. Equ., 2012 (): 1. 
[7] 
D. R. Anderson, R. I. Avery, J. Henderson, X. Liu and J. W. Lyons, Existence of a positive solution for a right focal discrete boundary value problem,, J. Difference Equ. Appl., 17 (2011), 1635. 
[8] 
J. Andres and V. Vlček, Green's functions for periodic and antiperiodic BVPs to secondorder ODEs,, Acta Univ. Palack. Olomuc. Fac. Rerum Natur. Math., 32 (1993), 7. 
[9] 
R. I. Avery, D. R. Anderson and J. Henderson, A topological proof and extension of the LeggettWilliams fixed point theorem,, Comm. Appl. Nonlinear Anal., 16 (2009), 39. 
[10] 
R. I. Avery, D. R. Anderson and J. Henderson, Existence of a positive solution to a right focal boundary value problem,, Electron. J. Qual. Theory Differ. Equ., 2010 (): 1. 
[11] 
R. I. Avery, P. W. Eloe and J. Henderson, A LeggettWillaims type theorem applied to a fourth order problem,, Commun. Appl. Anal., 16 (2012), 579. 
[12] 
C. Bai, On the solvability of antiperiodic boundary value problems with impulse,, Electron. J. Qual. Theory Differ. Equ., 2009 (): 1. 
[13] 
M. Benchohra, N. Hamidi and J. Henderson, Fractional differential equations with antiperiodic boundary conditions,, Numer. Funct. Anal. Optim., 34 (2013), 404. 
[14] 
D. Franco, J. J. Nieto and D. O'Regan, Antiperiodic boundary value problem for nonlinear first order ordinary differential equations,, Math. Inequal. Appl., 6 (2003), 477. 
[15] 
R. W. Leggett and L. R. Williams, Multiple positive fixed points of nonlinear operators on ordered Banach spaces,, Indiana Univ. Math. J., 28 (1979), 673. 
[16] 
X. Liu, J. T. Neugebauer and S. Sutherland, Application of a functional type compression expansion fixed point theorem for a right focal boundary value problem on a time scale,, Comm. Appl. Nonlinear Anal., 19 (2012), 25. 
[17] 
J. W. Lyons and J. T. Neugebauer, Existence of a positive solution for a right focal dynamic boundary value problem,, Nonlinear Dyn. Syst. Theory, 14 (2014), 76. 
[18] 
J. T. Neugebauer and C. L. Seelbach, Positive symmetric solutions of a second order difference equation,, Involve, 5 (2012), 497. 
[19] 
G. F. Roach, Green's Functions,, $2^{nd}$ edition, (1982). 
show all references
References:
[1] 
A. A. Altwaty and P. W. Eloe, The role of concavity in applications of Avery type fixed point theorems to higher order differential equations,, J. Math Inequal., 6 (2012), 79. 
[2] 
A. A. Altwaty and P. W. Eloe, Concavity of solutions of a $2n$th order problem with symmetry,, Opuscula Math., 33 (2013), 603. 
[3] 
D. R. Anderson and R. I. Avery, Fixed point theorem of cone expansion and compression of functional type,, J. Difference Equ. Appl., 8 (2002), 1073. 
[4] 
D. R. Anderson, R. I. Avery and J. Henderson, Functional expansioncompression fixed point theorem of LeggettWilliams type,, Electron. J. Differential Equations, 2010 (): 1. 
[5] 
D. R. Anderson, R. I. Avery, J. Henderson and X. Liu, Operator type expansioncompression fixed point theorem,, Electron. J. Differential Equations, 2011 (): 1. 
[6] 
D. R. Anderson, R. I. Avery, J. Henderson and X. Liu, Fixed point theorem utilizing operators and functionals,, Electron. J. Qual. Theory Differ. Equ., 2012 (): 1. 
[7] 
D. R. Anderson, R. I. Avery, J. Henderson, X. Liu and J. W. Lyons, Existence of a positive solution for a right focal discrete boundary value problem,, J. Difference Equ. Appl., 17 (2011), 1635. 
[8] 
J. Andres and V. Vlček, Green's functions for periodic and antiperiodic BVPs to secondorder ODEs,, Acta Univ. Palack. Olomuc. Fac. Rerum Natur. Math., 32 (1993), 7. 
[9] 
R. I. Avery, D. R. Anderson and J. Henderson, A topological proof and extension of the LeggettWilliams fixed point theorem,, Comm. Appl. Nonlinear Anal., 16 (2009), 39. 
[10] 
R. I. Avery, D. R. Anderson and J. Henderson, Existence of a positive solution to a right focal boundary value problem,, Electron. J. Qual. Theory Differ. Equ., 2010 (): 1. 
[11] 
R. I. Avery, P. W. Eloe and J. Henderson, A LeggettWillaims type theorem applied to a fourth order problem,, Commun. Appl. Anal., 16 (2012), 579. 
[12] 
C. Bai, On the solvability of antiperiodic boundary value problems with impulse,, Electron. J. Qual. Theory Differ. Equ., 2009 (): 1. 
[13] 
M. Benchohra, N. Hamidi and J. Henderson, Fractional differential equations with antiperiodic boundary conditions,, Numer. Funct. Anal. Optim., 34 (2013), 404. 
[14] 
D. Franco, J. J. Nieto and D. O'Regan, Antiperiodic boundary value problem for nonlinear first order ordinary differential equations,, Math. Inequal. Appl., 6 (2003), 477. 
[15] 
R. W. Leggett and L. R. Williams, Multiple positive fixed points of nonlinear operators on ordered Banach spaces,, Indiana Univ. Math. J., 28 (1979), 673. 
[16] 
X. Liu, J. T. Neugebauer and S. Sutherland, Application of a functional type compression expansion fixed point theorem for a right focal boundary value problem on a time scale,, Comm. Appl. Nonlinear Anal., 19 (2012), 25. 
[17] 
J. W. Lyons and J. T. Neugebauer, Existence of a positive solution for a right focal dynamic boundary value problem,, Nonlinear Dyn. Syst. Theory, 14 (2014), 76. 
[18] 
J. T. Neugebauer and C. L. Seelbach, Positive symmetric solutions of a second order difference equation,, Involve, 5 (2012), 497. 
[19] 
G. F. Roach, Green's Functions,, $2^{nd}$ edition, (1982). 
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