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Positive solution of Lighthill-type equations. (English) Zbl 1404.45002

Summary: We study a unique solvability of Volterra integral equations of Lighthill’s type subject to a positive solution on \([0,\infty)\). Also the asymptotics of the solution at the in finity is examined.

MSC:

45D05 Volterra integral equations
45M20 Positive solutions of integral equations
45M05 Asymptotics of solutions to integral equations
Full Text: DOI

References:

[1] Brunner, H., Volterra Integral Equations. An Introduction to Theory and Applications. Cambridge Univ. Press 2017. · Zbl 1376.45002
[2] Brunner, H., Pedas, A. and Vainikko, G., The piecewise polynomial collocation method for nonlinear weakly singular Volterra equations. Math. Comp. 68 (1999), 1079 – 1095. · Zbl 0941.65136
[3] Diethelm, K., The Analysis of Fractional Differential Equations. An Application-oriented Exposition Using Differential Operators of Caputo Type. Lect. Notes Math. 2004. Berlin: Springer 2010. · Zbl 1215.34001
[4] Friedman, A., On integral equations of Volterra type. J. Analyse Math. 11 (1963), 381 – 413. · Zbl 0134.31502
[5] Lighthill, J. M., Contributions to the theory of the heat transfer through laminar boundary layer. Proc. Roy. Soc. London. Ser. A. 202 (1950), 359 – 377. · Zbl 0038.11504
[6] Ling, R., Integral equations of Volterra type. J. Math. Anal. Appl. 64 (1978), 381 – 397. · Zbl 0403.45001
[7] Pedas, A. and Vainikko, G., The smoothness of solutions to nonlinear weakly singular integral equations. Z. Anal. Anwend. 13 (1994), 463 – 476. · Zbl 0803.45007
[8] Rebelo, M. and Diogo, T., A hybrid collocation method for nonlinear Volterra integral equation with weakly singular kernel. J. Comput. Appl. Math. 234 (2010), 2859 – 2869. · Zbl 1196.65202
[9] Vainikko, G., Cordial Volterra integral equations 1; 2. Numer. Funct. Anal. Optim. 30 (2009), 1145 – 1172; 31 (2010), 191 – 219. · Zbl 1195.45004
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