Some functional differential equations with both retarded and advanced arguments
DOI:
https://doi.org/10.33993/jnaat381-900Keywords:
functional-differential equations, boundary value problems, contraction's principle, Schauder's fixed point principleAbstract
In this paper we shall study a functional differential equation of mixed type. This equation is a generalization of some equations from medicine. Related to this equation we study the existence of the solution by contraction's principle and Schauder's fixed point theorem.Downloads
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Aronson, D.G. and Weinberger, H.F., Nonlinear diffusion in population genetics, combustion and nerve propagation, "Lectures Notes in Mathematics", 446, Springer-Verlag, Berlin, pp. 5-49, 1975, https://doi.org/10.1007/bfb0070595 DOI: https://doi.org/10.1007/BFb0070595
Mallet-Paret, J., The global structure of traveling waves in spatially discrete dynamical systems, J. Dyn. Diff Eq., 11, no. 1, pp. 49-127, 1999, https://doi.org/10.1023/a:1021841618074 DOI: https://doi.org/10.1023/A:1021841618074
Mallet-Paret, J., The Freedholm alternative for functional differential equations of mixed type, J. Dyn. Diff Eq., 11, no. 1, pp. 1-46, 1999, https://doi.org/10.1023/a:1021889401235 DOI: https://doi.org/10.1023/A:1021889401235
Mallet-Paret, J. and Lunel, S.V., Exponential dichotomies and Wiener-Hopf factorizations for mixed-type functional differential equations, 2001, www.dam.brown.edu/lcds/publications.textonly.html.
Precup, R., Some existence results for differential equations with both retarded and advanced arguments, Mathematica, 44 (67), no. 1, pp. 31-38, 2002.
Rus, I.A. and Dârzu-Ilea, V.A., First order functional-differential equations with both advanced and retarded arguments, Fixed Point Theory, 5, no. 1, pp. 103-115, 2004.
Rustichini, A., Functional differential equation of mixed type: The linear autonomous case, J. Dyn. Diff. Eq., 1, pp. 121-143, 1989, https://doi.org/10.1007/bf01047828 DOI: https://doi.org/10.1007/BF01047828
Rustichini, A., Hopf bifurcation for functional differential equation of mixed type, J. Dyn. Diff. Eq., 1, pp. 145-177, 1989, https://doi.org/10.1007/bf01047829 DOI: https://doi.org/10.1007/BF01047829
Schulman, L.S., Some differential difference equations containing both advance and retardation, J. Math. Phys., 15, pp. 195-198, 1974. DOI: https://doi.org/10.1063/1.1666641
Wu, J. and Zou, X., Asymptotic and periodic boundary value problems of mixed FDEs and wave solutions of lattice differential equations, J. Diff. Eq., 135, pp. 315-357, 1997, https://doi.org/10.1006/jdeq.1996.3232 DOI: https://doi.org/10.1006/jdeq.1996.3232
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