The existence of solutions to a Volterra integral equation

• Autorzy: Wojciech Mydlarczyk
• Języki publikacji: EN

Abstrakty

EN

We study the equation u = k∗g(u) with k such that ln k is convex or concave and g is monotonic. Some necessary and sufficient conditions for the existence of nontrivial continuous solutions u of this equation are given.

Słowa kluczowe

EN

the Volterra convolution type integral equations

Kategorie tematyczne

• 45D05: Volterra integral equations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 1996
• Tom: 64
• Numer: 2
• Strony: 175-182

Daty

wydano

1996

otrzymano

1995-11-16

Twórcy

autor

Wojciech Mydlarczyk

• Mathematical Institute, University of Wrocław, Pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland

Bibliografia

• [1] G. Gripenberg, On the uniqueness of solutions of Volterra equations, J. Integral Equations Appl. 2 (1990), 421-430.
• [2] R. K. Miller, Nonlinear Volterra Integral Equations, W. A. Benjamin, Menlo Park, Calif., 1971.
• [3] W. Mydlarczyk, The existence of nontrivial solutions of Volterra equations, Math. Scand. 68 (1991), 83-88.
• [4] W. Mydlarczyk, Remarks on a nonlinear Volterra equation, Ann. Polon. Math. 53 (1991), 227-232.
• [5] W. Okrasiński, Nontrivial solutions to nonlinear Volterra integral equations, SIAM J. Math. Anal. 4 (1991), 1007-1015.
• [6] W. Okrasiński, On a nonlinear Volterra integral equation, Math. Methods Appl. Sci. 8 (1986), 345-350.