Conference publications

Abstracts

XIV conference

On the uniqueness of zero solution of Hammerstein type integral inclusions

Nguyen Van Loi, Nguyen Thi Hoai

Russian, 394024, Voronezh, Sovietckai 2, hostel 1, VSPU, romm 234. tel. 8950 758 8561 Email: loitroc@yahoo.com

On the uniqueness of zero solution of Hammerstein type

integral inclusions

Consider problem on the existence of solution of the following inclusion

Let multimap satisfies the following conditions (see [1]):

for every the multifunction has a measurable selection;

the multimap is under semicontinuous for a.e. ;

denotes the collection of all linear operators in and let be an operator satisfying the following properties:

such that for all and a.e. ;

for every multifunction is measurable, ;

, multifunction is continuous by uniformly relatively to , т.е. , such that , from follow ,

for all .

Theorem 1. let kernel satisfies the conditions and multimap satisfies the conditions . Assume that:

there exits a function such that

, for all and a.e. ;

, where - constant from condition .

Then the integral inclusion (1) has only zero solution.

Let multimap is almost lower semicontinuous (see [1]).

Theorem 2. let kernel satisfies the conditions , and multimap is almost lower semicontinuous. Assume that, there exit a number and a function such that

,

for all and a.e. ;

.

Then the integral inclusion (1) has only zero solution.

Theorem 3. let kernel satisfies the conditions , multimap is almost lower semicontinuous and satisfies the conditions and . Then the integral inclusion (1) has only zero solution.

Литература

[1] Yu.G. Borissovich, B.D. Gelman, A.D. Myshkis and V.V. Obukhovskii, Introduction to the Theory of Multivalued Maps and Differential Inclusions, Voronezh Gos. Univ., Voronezh, 2005-216p.