The unique solution of some operator equations via fractional differential equations
Resumen
In this paper we consider the existence and uniqueness of positive solutions to the following operator equation in an ordered Banach space $E$
$$A(x,x)+B(x,x)=x,~x\in P,$$
where $P$ is a cone in $E$. We study an application for fractional differential equations.
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Guo D, Lakskmikantham, V: Coupled fixed points of nonlinear operators with applications. Nonlinear Anal. 11(5), 623-632(1987). https://doi.org/10.1016/0362-546X(87)90077-0
Guo D: Fixed points of mixed monotone operators with application. Appl. Anal. 34, 215-224(1988). https://doi.org/10.1080/00036818808839825
Kilbas A A, Srivastava H M, Trujillo, j j: Theory and applications of fractional differential equations. North-Holland Mathematics Studies. 204, 7-10(2006).
Liu. L, Zhang. X, Jiang. J, Wu. Y : The unique solution of a class of sum mixed monotone operator equations and its application to fractional boundary value problems J. Nonlinear Sci. Appl. 9 (2016), 2943-2958. https://doi.org/10.22436/jnsa.009.05.87
Podlubny I: Fractional Differential Equations. Academic Press, San Diego, (1999).
Sang, Y: Existence and uniqueness of fixed points for mixed monotone operators with perturbations, Electronic Journal of Differential Equations, 233(2013)1-16.
Sang, Y: A class of ϕ-concave operators and applications, Fixed Point Theory and Applications, vol. 2013, 2013. https://doi.org/10.1186/1687-1812-2013-274
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