Burton, Theodore A.; Purnaras, Ioannis K. Progressive contractions, product contractions, quadratic integro-differential equations. (English) Zbl 1484.45002 AIMS Math. 4, No. 3, 482-496 (2019). MSC: 45D05 34K05 45G05 47H10 PDFBibTeX XMLCite \textit{T. A. Burton} and \textit{I. K. Purnaras}, AIMS Math. 4, No. 3, 482--496 (2019; Zbl 1484.45002) Full Text: DOI
Burton, T. A. Positive solutions of scalar integral equations. (English) Zbl 1367.45002 Dyn. Syst. Appl. 25, No. 3, 351-364 (2016). Reviewer: Seenith Sivasundaram (Daytona Beach) MSC: 45M20 45D05 45G05 PDFBibTeX XMLCite \textit{T. A. Burton}, Dyn. Syst. Appl. 25, No. 3, 351--364 (2016; Zbl 1367.45002)
Burton, T. A.; Purnaras, I. K. Krasnoselskii’s unification, Volterra’s integrodifferential equation, and the method of Aizerman. (English) Zbl 1308.45006 Nonlinear Stud. 21, No. 1, 1-19 (2014). Reviewer: Dan-Mircea Borş (Iaşi) MSC: 45J05 47H10 45G10 45D05 PDFBibTeX XMLCite \textit{T. A. Burton} and \textit{I. K. Purnaras}, Nonlinear Stud. 21, No. 1, 1--19 (2014; Zbl 1308.45006) Full Text: Link
Burton, T. A. Liapunov theory for integral equations with singular kernels and fractional differential equations. (English) Zbl 1270.45010 Port Angeles, WA: Theodore Allen Burton (ISBN 978-1-4791-8180-3). xii, 379 p. (2012). Reviewer: I. V. Boikov (Penza) MSC: 45M10 45-02 45G05 45J05 45E10 34A09 34D20 PDFBibTeX XMLCite \textit{T. A. Burton}, Liapunov theory for integral equations with singular kernels and fractional differential equations. Port Angeles, WA: Theodore Allen Burton (2012; Zbl 1270.45010)
Burton, T. A.; Dwiggins, D. P. Resolvents of integral equations with continuous kernels. (English) Zbl 1233.45001 Nonlinear Stud. 18, No. 2, 293-305 (2011). Reviewer: Olof Staffans (Aalto) MSC: 45D05 45A05 PDFBibTeX XMLCite \textit{T. A. Burton} and \textit{D. P. Dwiggins}, Nonlinear Stud. 18, No. 2, 293--305 (2011; Zbl 1233.45001)
Burton, T. A. Fractional differential equations and Lyapunov functionals. (English) Zbl 1226.34004 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 74, No. 16, 5648-5662 (2011). Reviewer: Krishnan Balachandran (Coimbatore) MSC: 34A08 34D20 PDFBibTeX XMLCite \textit{T. A. Burton}, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 74, No. 16, 5648--5662 (2011; Zbl 1226.34004) Full Text: DOI
Burton, T. A.; Dwiggins, D. P. Smoothed integral equations. (English) Zbl 1215.45001 J. Math. Anal. Appl. 377, No. 1, 319-335 (2011). Reviewer: Alexander N. Tynda (Penza) MSC: 45G10 PDFBibTeX XMLCite \textit{T. A. Burton} and \textit{D. P. Dwiggins}, J. Math. Anal. Appl. 377, No. 1, 319--335 (2011; Zbl 1215.45001) Full Text: DOI
Burton, T. A. Lyapunov functionals, convex kernels, and strategy. (English) Zbl 1228.45008 Nonlinear Dyn. Syst. Theory 10, No. 4, 325-337 (2010). Reviewer: Martin Väth (Berlin) MSC: 45G10 45D05 45J05 45M05 PDFBibTeX XMLCite \textit{T. A. Burton}, Nonlinear Dyn. Syst. Theory 10, No. 4, 325--337 (2010; Zbl 1228.45008)
Burton, T. A.; Dwiggins, D. P. Resolvents, integral equations, limit sets. (English) Zbl 1224.45001 Math. Bohem. 135, No. 4, 337-354 (2010). MSC: 45D05 45A05 PDFBibTeX XMLCite \textit{T. A. Burton} and \textit{D. P. Dwiggins}, Math. Bohem. 135, No. 4, 337--354 (2010; Zbl 1224.45001) Full Text: EuDML
Burton, T. A.; Haddock, John R. Parallel theories of integral equations. (English) Zbl 1213.45001 Nonlinear Stud. 17, No. 3, 177-197 (2010). Reviewer: Olof Staffans (Åbo) MSC: 45D05 45M10 PDFBibTeX XMLCite \textit{T. A. Burton} and \textit{J. R. Haddock}, Nonlinear Stud. 17, No. 3, 177--197 (2010; Zbl 1213.45001)
Burton, T. A. A Liapunov functional for a linear integral equation. (English) Zbl 1193.45011 Electron. J. Qual. Theory Differ. Equ. 2010, Paper No. 10, 10 p. (2010). Reviewer: Li Xing (Yinchuan) MSC: 45D05 45G05 45A05 PDFBibTeX XMLCite \textit{T. A. Burton}, Electron. J. Qual. Theory Differ. Equ. 2010, Paper No. 10, 10 p. (2010; Zbl 1193.45011) Full Text: DOI EuDML EMIS
Burton, T. A.; Haddock, John R. Qualitative properties of solutions of integral equations. (English) Zbl 1184.45001 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 71, No. 11, 5712-5723 (2009). Reviewer: Olof Staffans (Åbo) MSC: 45D05 45M10 45J05 PDFBibTeX XMLCite \textit{T. A. Burton} and \textit{J. R. Haddock}, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 71, No. 11, 5712--5723 (2009; Zbl 1184.45001) Full Text: DOI
Burton, T. A. Integral equations, periodicity, and fixed points. (English) Zbl 1156.45003 Fixed Point Theory 9, No. 1, 47-65 (2008). Reviewer: Jin Liang (Shanghai) MSC: 45G05 45M15 47H10 PDFBibTeX XMLCite \textit{T. A. Burton}, Fixed Point Theory 9, No. 1, 47--65 (2008; Zbl 1156.45003)
Burton, T. A. Integral equations, \(L^{p}\)-forcing, remarkable resolvent: Lyapunov functionals. (English) Zbl 1129.45002 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 68, No. 1, 35-46 (2008). Reviewer: Gustaf Gripenberg (Hut) MSC: 45D05 45J05 45M10 PDFBibTeX XMLCite \textit{T. A. Burton}, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 68, No. 1, 35--46 (2008; Zbl 1129.45002) Full Text: DOI
Burton, T. A. Integral equations, large forcing, strong resolvents. (English) Zbl 1174.45001 Carpathian J. Math. 23, No. 1-2, 1-10 (2007). Reviewer: Roland Duduchava (Tbilisi) MSC: 45D05 45M10 PDFBibTeX XMLCite \textit{T. A. Burton}, Carpathian J. Math. 23, No. 1--2, 1--10 (2007; Zbl 1174.45001)
Burton, T. A. Integral equations, Volterra equations, and the remarkable resolvent: contractions. (English) Zbl 1090.45002 Electron. J. Qual. Theory Differ. Equ. 2006, Paper No. 2, 17 p. (2006). Reviewer: Olof Staffans (Åbo) MSC: 45D05 45A05 45P05 PDFBibTeX XMLCite \textit{T. A. Burton}, Electron. J. Qual. Theory Differ. Equ. 2006, Paper No. 2, 17 p. (2006; Zbl 1090.45002) Full Text: DOI EuDML EMIS
Burton, T. A. Stability by fixed point theory or Liapunov theory: a comparison. (English) Zbl 1061.47065 Fixed Point Theory 4, No. 1, 15-32 (2003). Reviewer: Sotiris K. Ntouyas (Ioannina) MSC: 47N20 47H10 34D20 34K20 PDFBibTeX XMLCite \textit{T. A. Burton}, Fixed Point Theory 4, No. 1, 15--32 (2003; Zbl 1061.47065)
Burton, T. A. Liapunov functionals, fixed points, and stability by Krasnoselskii’s theorem. (English) Zbl 1084.47522 Nonlinear Stud. 9, No. 2, 181-190 (2002). Reviewer: L. Hatvani (MR 2003e:34133) MSC: 47H10 34K20 47N20 PDFBibTeX XMLCite \textit{T. A. Burton}, Nonlinear Stud. 9, No. 2, 181--190 (2002; Zbl 1084.47522)
Burton, T. A. A fixed-point theorem of Krasnoselskii. (English) Zbl 1127.47318 Appl. Math. Lett. 11, No. 1, 85-88 (1998). MSC: 47H10 PDFBibTeX XMLCite \textit{T. A. Burton}, Appl. Math. Lett. 11, No. 1, 85--88 (1998; Zbl 1127.47318) Full Text: DOI
Burton, T. A.; Kirk, Colleen A fixed point theorem of Krasnoselskii-Schaefer type. (English) Zbl 0896.47042 Math. Nachr. 189, 23-31 (1998). Reviewer: J.Appell (Würzburg) MSC: 47H10 45M15 PDFBibTeX XMLCite \textit{T. A. Burton} and \textit{C. Kirk}, Math. Nachr. 189, 23--31 (1998; Zbl 0896.47042) Full Text: DOI
Burton, T. A. Basic neutral integral equations of advanced type. (English) Zbl 0888.45005 Nonlinear Anal., Theory Methods Appl. 31, No. 3-4, 295-310 (1998). Reviewer: J.Banaś (Rzeszów) MSC: 45G05 PDFBibTeX XMLCite \textit{T. A. Burton}, Nonlinear Anal., Theory Methods Appl. 31, No. 3--4, 295--310 (1998; Zbl 0888.45005) Full Text: DOI
Burton, T. A. Integral equations, implicit functions, and fixed points. (English) Zbl 0873.45003 Proc. Am. Math. Soc. 124, No. 8, 2383-2390 (1996). Reviewer: C.Corduneanu (Arlington) MSC: 45G10 47H10 PDFBibTeX XMLCite \textit{T. A. Burton}, Proc. Am. Math. Soc. 124, No. 8, 2383--2390 (1996; Zbl 0873.45003) Full Text: DOI
Burton, T. A. An integral equation of advanced and retarded type. (English) Zbl 0860.45006 Dyn. Syst. Appl. 5, No. 2, 183-187 (1996). Reviewer: G.Gripenberg (Helsinki) MSC: 45G10 45M15 PDFBibTeX XMLCite \textit{T. A. Burton}, Dyn. Syst. Appl. 5, No. 2, 183--187 (1996; Zbl 0860.45006)
Burton, T. A.; Furumochi, Tetsuo; Huang, Qichang Stability in several measures and a differential inequality for a partial integral equation. (English) Zbl 0845.45007 Nonlinear Anal., Theory Methods Appl. 25, No. 9-10, 885-898 (1995). Reviewer: D.M.Bors (Iaşi) MSC: 45K05 45M05 45M10 PDFBibTeX XMLCite \textit{T. A. Burton} et al., Nonlinear Anal., Theory Methods Appl. 25, No. 9--10, 885--898 (1995; Zbl 0845.45007) Full Text: DOI
Burton, T. A.; Furumochi, Tetsuo A stability theory for integral equations. (English) Zbl 0833.45009 J. Integral Equations Appl. 6, No. 4, 445-477 (1994). Reviewer: G.Karakostas (Ioannina) MSC: 45M10 45G10 45M05 PDFBibTeX XMLCite \textit{T. A. Burton} and \textit{T. Furumochi}, J. Integral Equations Appl. 6, No. 4, 445--477 (1994; Zbl 0833.45009) Full Text: DOI
Burton, T. A.; Furumochi, Tetsuo Periodic solutions of Volterra equations and attractivity. (English) Zbl 0811.45001 Dyn. Syst. Appl. 3, No. 4, 583-598 (1994). Reviewer: G.Gripenberg (Espoo) MSC: 45G05 45G10 45M15 PDFBibTeX XMLCite \textit{T. A. Burton} and \textit{T. Furumochi}, Dyn. Syst. Appl. 3, No. 4, 583--598 (1994; Zbl 0811.45001)
Burton, T. A. Differential inequalities and existence theory for differential, integral, and delay equations. (English) Zbl 0809.34006 Liu, Xinzhi (ed.) et al., Comparison methods and stability theory. The Symposium was held in Waterloo, Ontario, Canada, June 3-6, 1993. Proceedings. Basel: Marcel Dekker. Lect. Notes Pure Appl. Math. 162, 35-56 (1994). Reviewer: S.K.Lakshmana Rao (Bangalore) MSC: 34A12 34A40 34K05 45J05 PDFBibTeX XMLCite \textit{T. A. Burton}, Lect. Notes Pure Appl. Math. 162, 35--56 (1994; Zbl 0809.34006)
Burton, Theodore A. Liapunov functionals and periodicity in integral equations. (English) Zbl 0808.45009 Tôhoku Math. J., II. Ser. 46, No. 2, 207-220 (1994). Reviewer: O.Staffans (Espoo) MSC: 45G10 45M05 45M15 PDFBibTeX XMLCite \textit{T. A. Burton}, Tôhoku Math. J. (2) 46, No. 2, 207--220 (1994; Zbl 0808.45009) Full Text: DOI
Burton, T. A. Boundedness and periodicity in integral and integro-differential equations. (English) Zbl 0871.45003 Differ. Equ. Dyn. Syst. 1, No. 2, 161-172 (1993). MSC: 45D05 45J05 45M05 45M15 PDFBibTeX XMLCite \textit{T. A. Burton}, Differ. Equ. Dyn. Syst. 1, No. 2, 161--172 (1993; Zbl 0871.45003)
Burton, T. A.; Huang, Quichang; Mahfoud, W. E. Liapunov functionals of convolution type. (English) Zbl 0587.34042 J. Math. Anal. Appl. 106, 249-272 (1985). Reviewer: S.Kono MSC: 34D20 45J05 PDFBibTeX XMLCite \textit{T. A. Burton} et al., J. Math. Anal. Appl. 106, 249--272 (1985; Zbl 0587.34042) Full Text: DOI
Burton, T. A. Phase spaces and boundedness in Volterra equations. (English) Zbl 0585.45002 J. Integral Equations 10, Suppl., 61-72 (1985). Reviewer: G.Gripenberg MSC: 45J05 45M10 PDFBibTeX XMLCite \textit{T. A. Burton}, J. Integral Equations 10, 61--72 (1985; Zbl 0585.45002)
Burton, T. A. Periodicity and limiting equations in Volterra systems. (English) Zbl 0581.45007 Boll. Unione Mat. Ital., VI. Ser., C, Anal. Funz. Appl. 4, 31-39 (1985). Reviewer: Enhao Yang MSC: 45J05 45M99 PDFBibTeX XMLCite \textit{T. A. Burton}, Boll. Unione Mat. Ital., VI. Ser., C, Anal. Funz. Appl. 4, 31--39 (1985; Zbl 0581.45007)
Burton, T. A.; Huang, Qichang; Mahfoud, W. E. Rate of decay of solutions of Volterra equations. (English) Zbl 0579.45008 Nonlinear Anal., Theory Methods Appl. 9, 651-663 (1985). Reviewer: O.Staffans MSC: 45J05 45G10 45M10 PDFBibTeX XMLCite \textit{T. A. Burton} et al., Nonlinear Anal., Theory Methods Appl. 9, 651--663 (1985; Zbl 0579.45008) Full Text: DOI
Burton, T. A.; Mahfoud, W. E. Instability and stability in Volterra equations. (English) Zbl 0529.45006 Trends in theory and practice of nonlinear differential equations, Proc. int. Conf., Arlington/Tex. 1982, Lect. Notes Pure Appl. Math. 90, 99-104 (1984). MSC: 45J05 45M10 PDFBibTeX XML
Burton, T. A. Stability theory for Volterra equations. (English) Zbl 0422.45009 J. Differ. Equations 32, 101-118 (1979). MSC: 45M10 45D05 45J05 PDFBibTeX XMLCite \textit{T. A. Burton}, J. Differ. Equations 32, 101--118 (1979; Zbl 0422.45009) Full Text: DOI