ABSTRACT

A self-contained account of integro-differential equations of the Barbashin type and partial integral operators. It presents the basic theory of Barbashin equations in spaces of continuous or measurable functions, including existence, uniqueness, stability and perturbation results. The theory and applications of partial integral operators and linea

chapter |10 pages

Introduction

chapter |7 pages

+ is

chapter |16 pages

equations Banach

chapter |2 pages

§ 2. Barbashin equations in the space C

+l'lk(

chapter |18 pages

BY-valued

chapter |7 pages

< s S

"j-l)

chapter |5 pages

< (0),

chapter |1 pages

.cHL,)

.cHL,)

chapter |17 pages

IAIIBI

chapter |1 pages

tl,""

·1',.-1

chapter |4 pages

Barbashin equations in

chapter |33 pages

0,

chapter |4 pages

: u(T)}

chapter |14 pages

Continuous dependence parameters

chapter |25 pages

Bounded and periodic

chapter |2 pages

JIT c(t,s)dt > and x

chapter |12 pages

Degenerate

chapter |6 pages

Stationary boundary-value problems

chapter |16 pages

all(t,s)EQ,

chapter |16 pages

< g(I,8}

chapter |1 pages

= c(t,s)y(t,s)

chapter |1 pages

Ic(t, s)x(t,s)y(t, s)d(pv)(t,s)

chapter X|2 pages

'. X'

chapter |3 pages

tE or E The space

chapter |6 pages

Operators in with mixed norm

lIullullllv.

chapter i|2 pages

(t,r)

II(t,

chapter |3 pages

-. -.

chapter |2 pages

Y= LLL

chapter |16 pages

if if

chapter |3 pages

Partial integral operators

chapter |2 pages

r(:= Iv

chapter |1 pages

> > > >

chapter |4 pages

r(t,s)

chapter |1 pages

cis A:=

chapter |1 pages

o(Pn)n

chapter |2 pages

en)"

chapter |3 pages

"i(t,

chapter |6 pages

< t,

chapter |2 pages

{I/(

chapter |1 pages

< (,

chapter |1 pages

§ 14. Spectral properties

chapter |14 pages

¢ A) z X)

cllzll

chapter |6 pages

(K -.\1)(x

chapter |3 pages

> + u

chapter |1 pages

(j ...

chapter |5 pages

eij'" .,

chapter |4 pages

"liE

chapter |1 pages

E[ak(a)

chapter |5 pages

J

chapter |1 pages

< r(1(K).

chapter |3 pages

ill:

Linear partial integral equations

chapter |1 pages

r)f(r,

chapter |5 pages

ill:

chapter |1 pages

n(t,s,r,u)

chapter |4 pages

N)zf,

chapter l|1 pages

(t-

[-1,1],5

chapter |2 pages

IL,,(T K)-l

chapter |3 pages

fi; ) < °i

chapter |6 pages

,p,;

(lij)

chapter |12 pages

Generalized equations of Barbashin type

chapter |6 pages

Nonlinear equations and operators

chapter |2 pages

[-l,t]

chapter 17|6 pages

'

chapter |14 pages

f«I,.):=

chapter |2 pages

§ 18. The Newton-Kantorovich method

chapter |10 pages

swar

chapter |15 pages

rand

chapter |10 pages

Applications of Barbashin equations

chapter |13 pages

Fare

chapter |6 pages

< -1 <

([-l,l])

chapter |7 pages

< (0)

chapter |7 pages

o0'(M 1 )

chapter |13 pages

M(t)

chapter |50 pages

References

chapter |1 pages

List

Symbols

chapter |7 pages

6l(X)