On uniqueness and successive approximations in the Darboux problem for the equation
B. Palczewski (1965)
Annales Polonici Mathematici
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B. Palczewski (1965)
Annales Polonici Mathematici
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T. Chantladze, Nodar Kandelaki, Alexander Lomtatidze (2001)
Archivum Mathematicum
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Integral criteria are established for and , where is the space of solutions of the equation satisfying the condition
Cristinel Mortici (2006)
Czechoslovak Mathematical Journal
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Let be a -contraction on a Banach space and let be an almost -contraction, i.e. sum of an -contraction with a continuous, bounded function which is less than in norm. According to the contraction principle, there is a unique element in for which If moreover there exists in with , then we will give estimates for Finally, we establish some inequalities related to the Cauchy problem.
Marko Švec (1997)
Archivum Mathematicum
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The paper deals with the periodic boundary value problem (1) , , (2) , , where , , , , , and are continuous on , , , , {nonempty convex compact subsets of }, . The existence of such periodic solution is proven via Ky Fan’s fixed point theorem.