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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:
47H10Fixed point theorems for nonlinear operators on topological linear spaces
45G10Nonsingular nonlinear integral equations
47N20Applications of operator theory to differential and integral equations
65J15Equations 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