Vvedenie v teoriyu mnogomernykh integral'nykh uravneniy tipa Vol'terra: s fiksirovannymi singulyarnymi i sverkhsingulyarnymi ya,Used

Vvedenie v teoriyu mnogomernykh integral'nykh uravneniy tipa Vol'terra: s fiksirovannymi singulyarnymi i sverkhsingulyarnymi ya,Used

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Monografiya posvyashchena issledovaniyu dvumernykh, trekhmernykh i nekotorykh mnogomernykh integral'nykh uravneniy tipa Vol'terra s singulyarnymi i sverkhsingulyarnymi granichnymi oblastyami v yadrakh. V opredelennykh sluchayakh, udaetsya nayti yavnyy vid resheniya dannykh uravneniy. V zavisimosti ot znaka parametrov, prisutstvuyushchikh v integral'nom uravnenii, vydeleny sluchai, kogda rassmatrivaemye integral'nye uravneniya imeyut edinstvennye reshenie. V sluchayakh, kogda obshchee reshenie integral'nogo uravneniya soderzhit proizvol'nye funktsii, vpervye dlya integral'nogo uravneniya stavyatsya i issleduyutsya razlichnye granichnye zadachi s vesami. Takzhe issledovany sopryazhennye dvumernye integral'nye uravneniya. Vydeleny sluchai, kogda dlya razreshimosti sopryazhennogo integral'nogo uravneniya trebuetsya beskonechnoe chislo usloviy razreshimosti. Dlya nmernogo model'nogo i nemodel'nogo integral'nogo uravneniya v nmernom paralelopipede, opredeleny usloviya na parametry, pri kotorom reshenie integral'nogo uravneniya nakhoditsya v yavnom vide. V etom sluchae, v zavisimosti ot znaka parametrov, prisutstvuyushchikh v odnokratnykh singulyarnykh integral'nykh operatorov, vsego polucheny 2n integral'nykh predstavleniy mnogoobraziya resheniy.

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