Geodesic
Gradient method for solving nonlinear discrete and integral equations with difference kernels
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh spring mathematical school “Modern methods of the theory of boundary-value problems. Pontryagin readings – XXX”. Voronezh, May 3-9, 2019. Part 3, Tome 192 (2021), pp. 26-37

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The method of potential monotonic operators (called also the Browder–Minty method) is used to prove global theorems on the existence and uniqueness of solutions for discrete and integral equations with difference kernels and odd-power nonlinearities. Using the gradient method (or the steepest descent method), we construct successive approximations that converge to the solutions mentioned with respect to the norm.
Keywords: monotonic operator, potential operator, nonlinear discrete equation, nonlinear integral equation. 
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     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
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S. N. Askhabov. Gradient method for solving nonlinear discrete and integral equations with difference kernels. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh spring mathematical school “Modern methods of the theory of boundary-value problems. Pontryagin readings – XXX”. Voronezh, May 3-9, 2019. Part 3, Tome 192 (2021), pp. 26-37. http://geodesic.mathdoc.fr/item/INTO_2021_192_a2/