Volume 67 | Issue 6 | Year 2021 | Article Id. IJMTT-V67I6P513 | DOI : https://doi.org/10.14445/22315373/IJMTT-V67I6P513
In this paper, we proved an existence theorem for ordinary functional differential equations with periodic boundary conditions via a fixed point theorem in Banach algebras, some mixed generalized Lipschitz and caratheodory conditions.
[1] B.C.Dhage, S.N.Salunkhe, Ravi Agrawal and W. Zhange, A functional differential equations in Banach algebras, Math. Ineqe.Appl.8 (1)(2005) 89-99.
[2] B.C.Dhage, A nonlinear alternative in Banach algebras with application to functional differential equation, Nonlinear funct. Annal. and Appl. 8(40)(2004) 563-575.
[3] B.C.Dhage, Some algebraic fixed point theorem for multi-valued mapping with applications, Disc.Math.Diff.Incls.control and optimization (2006), 45-55.
[4] B.C.Dhage, Fixed point theorem in order Banach algebras and applications, PanAmer.Math.J.9 (4) (1999), 93-102.
[5] B.C.Dhage and D.O’Regan, Fixed point theorem in Banach algebra with applications to nonlinear integral equations, Funct.Diff.Equ.7 (3-4) (2000) 259-267.
[6] Salunkhe S.N.,Timol M.G., Continuity and compactness results for differential operators in Banach space,Int.eJ.Math.Engi.127(2011) 1155-1160.
[7] S.N.Salunkhe, M.G.Timol, Existence theorem for first order ordinary functional differential equation with periodic boundary conditions, Gen.Math.Notes, 1(2) (2010) 185-194.
[8] J.Dugundji and A.Granas, Fixed point theorem, Monographic Math.Warsaw (1982).
[9] A.Granas,R.B.Guenther,J.W.Lec, Some general existence principles for carathèodory theory of nonlinear diff. equations,J. Math. pures. et appl.70 (1991) 153-196.
[10] D.Guo and V.Laxshmikantham, Nonlinear problems in abstract spaces, Academic Press, New York, (1988).
[11] E.Zeidler, Nonlinear functional Analysis Part-I, Springer Verlag, New York, (1985).
[12] Nieto J.J, Basic theory of Non-resonance impulsive periodic problems of first order, J.Math.anal.appl.205(1997) 423-433.
[13] Nieto J.J, Periodic boundary value problems for first order impulsive ODEs, Nonlinear Anal.51(2002) 1223-1232.
S.N.Salunkhe, "Ordinary Functional Differential Equations With Periodic Boundary Conditions Involving Caratheodory Condition," International Journal of Mathematics Trends and Technology (IJMTT), vol. 67, no. 6, pp. 119-124, 2021. Crossref, https://doi.org/10.14445/22315373/IJMTT-V67I6P513