Abstract
In this paper, the fixed point theorem of increasing operator with non-continuity is utilized to discuss the existence and uniqueness of positive solution for a class of nonlinear Volterra integral equations. An important condition of continuity can be replaced by weak condition.
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J., Goncerzewicz. H., Marcinkowska, W., Okrasinski and K., Tabisz, On the percolation of water from a cylindrical reservoir into the surrounding soil.,Zastas. Mat.,16 (1978), 249–261.
J. J., Keller, Propagation of simple nonlinear waves in gas filled tubes with friction,Z. Angew. Math. Phys.,32 (1981), 170–181.
P. J., Bushell and W., Okrasinski, Non-linear Volterra equations with convolution kernel,J. London. Math. Soc.,41, 2 (1990), 503–510.
P. J., Bushell and W., Okrasinski, Uniqueness of solutions for a class of non-linear Volterra integral equations with convolution kernel,Math. Proc. Camb. Phil. Soc.,106 (1989), 547–552.
Sun, Jingxian, Fixed point theorem of non-continuous increasing operator and its application on non-linear equations,Acta Mathematica Sinica,31, 1 (1988), 101–107.
Guo Dajun,Non-linear Function Analysis, Shandong Science and Technology Press (1985), 234–243.
Guo, Dajun and V., Lakshmikanthan,Non-linear Problems in Asbtract Cones, Notes and Reports in Mathematics Science and Engineering. Vol.5 (1988), 1–17.
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Communicated by Ding Xieping
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Wei, D. Uniqueness of solutions for a class of non-linear volterra integral equations without continuity. Appl Math Mech 18, 1191–1196 (1997). https://doi.org/10.1007/BF00713721
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DOI: https://doi.org/10.1007/BF00713721