Ferreira, Rui A. C. Existence of solutions to some retarded integrodifferential equations via the topological transversality theorem. (English) Zbl 1182.26032 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 72, No. 6, 3062-3068 (2010). Summary: We prove the existence of solutions to some retarded integrodifferential equations under some suitable conditions on the involved functions. Some applications of our results are also provided. MSC: 26D10 Inequalities involving derivatives and differential and integral operators 26D15 Inequalities for sums, series and integrals 45J05 Integro-ordinary differential equations Keywords:integral inequalities; retarded equation; topological transversality PDFBibTeX XMLCite \textit{R. A. C. Ferreira}, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 72, No. 6, 3062--3068 (2010; Zbl 1182.26032) Full Text: DOI References: [1] Constantin, A., Global existence of solutions for perturbed differential equations, Ann. Mat. Pura Appl., 168, 4, 237-299 (1995) [2] Constantin, A., Solutions globales d’équations différentielles perturbées, C. R. Acad. Sci. Paris, 320, 11, 1319-1322 (1995), MR1338279 (96e:34016) · Zbl 0839.34002 [3] Granas, A.; Dugundji, J., Fixed Point Theory (2003), Springer: Springer New York, MR1987179 (2004d:58012) · Zbl 1025.47002 [4] Constantin, A., Topological transversality: Application to an integrodifferential equation, J. Math. Anal. Appl., 197, 3, 855-863 (1996), MR1373084 (97a:34177) · Zbl 0855.45006 [5] Lipovan, O., A retarded Gronwall-like inequality and its applications, J. Math. Anal. Appl., 252, 1, 389-401 (2000), MR1797863 (2001k:26028) · Zbl 0974.26007 [6] Mydlarczyk, W.; Okrasiński, W., Nonlinear Volterra integral equations with convolution kernels, Bull. Lond. Math. Soc., 35, 4, 484-490 (2003) · Zbl 1026.45007 [7] Okrasiński, W., On the existence and uniqueness of nonnegative solutions of a certain nonlinear convolution equation, Ann. Polon. Math., 36, 1, 61-72 (1979) · Zbl 0412.45006 [8] Okrasiński, W., On a nonlinear convolution equation occurring in the theory of water percolation, Ann. Polon. Math., 37, 3, 223-229 (1980) · Zbl 0451.45004 [9] Constantin, A., Monotone iterative technique for a nonlinear integral equation, J. Math. Anal. Appl., 205, 1, 280-283 (1997) · Zbl 0878.45006 [10] Constantin, A., Nonlinear alternative: Application to an integral equation, J. Appl. Anal., 5, 1, 119-123 (1999) · Zbl 0930.45005 [11] Lipovan, O., Asymptotic properties of solutions to some nonlinear integral equations of convolution type, Nonlinear Anal., 69, 7, 2179-2183 (2008) · Zbl 1151.45011 [12] Lipovan, O., On the asymptotic behavior of solutions to some nonlinear integral equations of convolution type, Dyn. Contin. Discrete Impuls. Syst. Ser. A Math. Anal., 16, 2, 147-154 (2009) · Zbl 1184.45004 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.