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Monotone iterative technique for a nonlinear integral equation. (English) Zbl 0878.45006
The monotone iterative technique is used to prove the existence of positive solutions to nonlinear integral equations of Volterra type. In a special case the author proves the uniqueness of the solution.

45M20Positive solutions of integral equations
45G10Nonsingular nonlinear integral equations
45L05Theoretical approximation of solutions of integral equations
Full Text: DOI
[1] Bear, J.: Dynamics of fluids in porous media. (1972) · Zbl 1191.76001
[2] Constantin, A.: Solutions globales d’équations différentielles perturbées. C. R. Acad. sci. Paris 320, 1319-1322 (1995) · Zbl 0839.34002
[3] Constantin, A.: Topological transversality: application to an integrodifferential equation. J. math. Anal. appl. 197, 855-863 (1996) · Zbl 0855.45006
[4] Dieudonné, J.: Foundations of modern analysis. (1969) · Zbl 0176.00502
[5] Okrasinski, W.: On a non-linear convolution equation occurring in the theory of water percolation. Ann. polon. Math. 37, 223-229 (1980) · Zbl 0451.45004
[6] Sansone, G.; Conti, R.: Non-linear differential equations. (1964) · Zbl 0128.08403