TY - JOUR AU - Zhang, Xinqiu AU - Liu, Lishan AU - Wu, Yonghong PY - 2017 TI - Existence and uniqueness of iterative positive solutions for singular Hammerstein integral equations JO - Journal of Nonlinear Sciences and Applications SP - 3364--3380 VL - 10 IS - 7 AB - In this article, we study the existence and the uniqueness of iterative positive solutions for a class of nonlinear singular integral equations in which the nonlinear terms may be singular in both time and space variables. By using the fixed point theorem of mixed monotone operators in cones, we establish the conditions for the existence and uniqueness of positive solutions to the problem. Moreover, we derive various properties of the positive solutions to the equation and establish their dependence on the model parameter. The theorem obtained in this paper is more general and complements many previous known results including singular and nonlinear cases. Application of the results to the study of differential equations are also given in the article. SN - ISSN 2008-1901 UR - http://dx.doi.org/10.22436/jnsa.010.07.01 DO - 10.22436/jnsa.010.07.01 ID - Zhang2017 ER - TY - JOUR TI - On fourth order boundary value problems arising in beam analysis AU - R. P. Agarwal JO - Differential Integral Equations PY - 1989 DA - 1989// VL - 2 ID - Agarwal1989 ER - TY - JOUR TI - Iterative methods for a fourth order boundary value problem AU - R. P. Agarwal AU - Y. M. Chow JO - J. Comput. Appl. Math. PY - 1984 DA - 1984// VL - 10 ID - Agarwal1984 ER - TY - JOUR TI - Positive solutions of nonlinear fractional differential equations with integral boundary value conditions AU - A. Cabada AU - G.-T. Wang JO - J. Math. Anal. Appl. PY - 2012 DA - 2012// VL - 389 ID - Cabada2012 ER - TY - JOUR TI - Existence and uniqueness of solutions for singular integral equation AU - Z.-W. Cao AU - D.-Q. Jiang AU - C.-J. Yuan AU - D. 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