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XIV-ая конференция

Об единственности нулевого решения интегральных включений типа Гаммерштейна

Нгуен Ван Лой, Нгуен Тхи Хоай

Россия, 394024, г. Воронеж, ул. Советская, дом 2, общ.№1 ВГПУ, ком. 234 Тел. 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.