Geodesic
New Equations of Convolution Type Obtained by Replacing the Integral by Its Maximum
Matematičeskie zametki, Tome 71 (2002) no. 1, pp. 18-26.

Voir la notice de l'article provenant de la source Math-Net.Ru

We study the nonlinear equation $$ \max _{\gamma \in \mathbb R}g(\gamma )|\cos (\gamma -\alpha )| =f(\alpha ), $$ where $f(\alpha)$ is a given function and $g(\gamma)$ is the unknown function, to be found in the class of nonnegative continuous $\pi$-periodic functions. This equation arose in the context of an applied problem dealing with the construction of a hydrofoil from given pressure envelopes. Necessary and sufficient conditions for the solvability of the equation, an explicit description of the solution set, and a comparison theorem under changes of the right-hand sides are obtained. Some possible ways of generalization are indicated. 
@article{MZM_2002_71_1_a1,
     author = {F. G. Avkhadiev and D. V. Maklakov},
     title = {New {Equations} of {Convolution} {Type} {Obtained} by {Replacing} the {Integral} by {Its} {Maximum}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {18--26},
     publisher = {mathdoc},
     volume = {71},
     number = {1},
     year = {2002},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2002_71_1_a1/}
}
TY  - JOUR
AU  - F. G. Avkhadiev
AU  - D. V. Maklakov
TI  - New Equations of Convolution Type Obtained by Replacing the Integral by Its Maximum
JO  - Matematičeskie zametki
PY  - 2002
SP  - 18
EP  - 26
VL  - 71
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2002_71_1_a1/
LA  - ru
ID  - MZM_2002_71_1_a1
ER  - 
%0 Journal Article
%A F. G. Avkhadiev
%A D. V. Maklakov
%T New Equations of Convolution Type Obtained by Replacing the Integral by Its Maximum
%J Matematičeskie zametki
%D 2002
%P 18-26
%V 71
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2002_71_1_a1/
%G ru
%F MZM_2002_71_1_a1
F. G. Avkhadiev; D. V. Maklakov. New Equations of Convolution Type Obtained by Replacing the Integral by Its Maximum. Matematičeskie zametki, Tome 71 (2002) no. 1, pp. 18-26. http://geodesic.mathdoc.fr/item/MZM_2002_71_1_a1/

[1] Avkhadiev F. G., Maklakov D. V., “Kriterii razreshimosti zadachi postroeniya profilei po zadannoi kavitatsionnoi diagramme”, Izv. vuzov. Matem., 1994, no. 7, 3–12 | MR | Zbl

[2] Avkhadiev F. G., Maklakov D. V., “Analiticheskii metod postroeniya gidroprofilei po zadannoi kavitatsionnoi diagramme”, Dokl. RAN, 343:2 (1995), 195–197 | MR | Zbl

[3] Avhadiev F. G., Maklakov D. V., “A theory of pressure envelope for hydrofoils”, J. Ship Technology Research, 42:2 (1995), 81–102 | MR

[4] Levin B. Ya., Raspredelenie kornei tselykh funktsii, GITTL, M., 1956

[5] Khardi G. G., Littlvud Dzh. E., Polia G., Neravenstva, IL, M., 1948