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Applying a fixed point theorem of Krasnosel’skii type to the existence of asymptotically stable solutions for a Volterra-Hammerstein integral equation. (English) Zbl 1214.47049
Summary: Using a fixed point theorem of Krasnosel’skii type, the paper proves the existence of asymptotically stable solutions for a Volterra-Hammerstein integral equation.
##### MSC:
 47H10 Fixed point theorems for nonlinear operators on topological linear spaces 45G10 Nonsingular nonlinear integral equations 47N20 Applications of operator theory to differential and integral equations 65J15 Equations with nonlinear operators (numerical methods)
##### References:
 [1] Corduneanu, C.: Integral equations and applications, (1991) [2] Avramescu, C.; Vladimirescu, C.: An existence result of asymptotically stable solutions for an integral equation of mixed type, Electronic J. Qualitative theory differ. Equ. 25, 1-6 (2005) · Zbl 1104.47063 · doi:emis:journals/EJQTDE/2005/200525.html [3] Avramescu, C.; Vladimirescu, C.: Asymptotic stability results for certain integral equations, Electronic J. Differ. equ. 126, 1-10 (2005) · Zbl 1099.47061 · doi:emis:journals/EJDE/Volumes/2005/126/abstr.html [4] Ngoc, L. T. P.; Long, N. T.: On a fixed point theorem of Krasnoselskii type and application to integral equations, Fixed point theory appl. 2006 (2006) · Zbl 1143.47302 · doi:10.1155/FPTA/2006/30847 [5] Hoa, L. H.; Schmitt, K.: Periodic solutions of functional differential equations of retarded and neutral types in Banach spaces, Boundary value problems for functional differential equations, 177-185 (1995) · Zbl 0842.34082 [6] Lang, S.: Analysis II, (1969) · Zbl 0176.00504