On some relations among the solutions of the linear volterra integral equations with convolution kernel
Küçük Resim Yok
Tarih
2012
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Erişim Hakkı
info:eu-repo/semantics/closedAccess
Özet
The sufficient conditions for y1(x) ? y2(x) were given in [1] such that ym(x) = CMEX10.-1.integraltext fm(x) + ? x a Km(x, t)ym(t)dt, (m = 1, 2) and x ? [a, b]. Some properties such as positivity, boundedness and monotonicity of the solution of the linear Volterra integral equation of the form CMEX10.-1.integraltext t - f(t) = 1 - ? t 0 K(t - ?)f(?)d? = 1 - K f, (0 ? t < ?) were obtained, without solving this equation, in [3, 4, 5, 6]. Also, the boundaries for functions f', f'',.., f(n), (n ? N) defined on the infinite interval [0, ?) were found in [7, 8]. In this work, for the given equation f(t) = 1 - K * f and n ? 2, it is derived that there exist the functions L2, L3,.., Ln which can be obtained by means of K and some inequalities among the functions f, h2, h3,.., hi for i = 2, 3,.., n are satisfied on the infinite interval [0, ?), where hi is the solution of the equation hi(t) = 1 - Li * hi and n is a natural number. © 2012 Austral Internet Publishing.
Açıklama
Anahtar Kelimeler
Convolution theorem, Equivalence theorem, Linear Volterra integral equations with convolution kernel
Kaynak
Australian Journal of Mathematical Analysis and Applications
WoS Q Değeri
Scopus Q Değeri
Q4
Cilt
9
Sayı
2
