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National Repository of Grey Literature

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Mountain Pass Theorem and its applications Příhoda, Vojtěch ; Černý, Robert (advisor) ; Vlasák, Václav (referee) Cílem této práce je formulovat a dokázat Větu o horském sedle a ukázat příklady její aplikace tak, aby student třetího ročníku matematiky nebo fy- ziky, jenž absolvoval alespoň úvodní kurs funkcionální analýzy, byl schopen práci porozumět. D·kaz Věty o horském sedle provedeme s pomocí Ekelan- dova variačního principu, který si rovněž formulujeme a dokážeme. Následně si ukážeme dva příklady její aplikace na d·kaz existence netriviálního sla- bého řešení eliptické parciální diferenciální rovnice obsahující nelinearitu se subkritickým r·stem. 1 Detailed record

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