Luận văn Thạc sĩ Toán học: Mở rộng và ứng dụng bổ đề Gronwall - Bellman

D~I HQC Quac GIA TP. HO CHi MINH<br /> TRUONG DAI HOC KHOA HOC TU NHIEN<br /> ..<br /> ..<br /> <br /> HoANG THANH LONG<br /> <br /> MO RaNGvA UNGDUNG<br /> .<br /> .<br /> ~<br /> BODE GRONWALL-BELLMAN<br /> ~<br /> <br /> Chuyen nganh : Toan Ghii Tich<br /> <br /> Ma s6<br /> <br /> : 1.01.01<br /> LUA.N VAN THAC 51 ToAN HOC<br /> .<br /> .<br /> .<br /> <br /> NGUOI HUaNG DAN KHOA HOC:<br /> PGS. TS. NGDYE N DINH PHU<br /> _.. .<br /> I;Ht.~H.TlI' NHIEN<br /> ~.::(.";<br /> <br /> lTHtJ \t1~N<br /> 001103<br /> I.<br /> <br /> ....<br /> <br /> TP. Hfi CHi MINH - 2005<br /> <br /> 1<br /> MlJ ri)ng va ung d~ng Bd d~ Gronwall-Bellman<br /> <br /> Hoang Thanh Long<br /> <br /> MUCLUC<br /> .<br /> .<br /> Trang<br /> M1).C 11).c.<br /> <br /> 1<br /> <br /> Loi Carn do.<br /> <br /> 3<br /> <br /> Danh rn1).ccac ky hi~u.<br /> <br /> 4<br /> <br /> -<br /> <br /> 5<br /> <br /> Chu'dng 0 T6ng quail.<br /> Chu'dng 1 - B6 dS Gronwall-<br /> <br /> Bellman va mQt sf{<br /> 7<br /> <br /> m(j rQng d(;lngtuy€n tinh.<br /> Chu'dng 2 - MQt sf{m(j rQng d(;lngphi tuy€n.<br /> <br /> 13<br /> <br /> Chu'dng 3 - MQt sf{ m(j rQng d(;lng ham exponent.<br /> <br /> 34<br /> <br /> Chu'dng 4 - MQt sf{ling dl;!ng<br /> <br /> 38<br /> <br /> §4.1. Sl;!' uy nha't nghi~m cua phuong trlnh vi<br /> d<br /> 38<br /> <br /> phan va tich phan.<br /> §4.2. Sl;!'lien tl;!Ccua nghi~m theo diSu ki~n<br /> <br /> 43<br /> <br /> d~u va theo v€ phai.<br /> <br /> 45<br /> <br /> §4. 3. £hinh gia tinh b~ ch~n cua nghi~m.<br /> <br /> §4.4. Sai l~ch nghi~m hai phuong trlnh vi phan. 48<br /> §4.5. Sl;!'phl;! thuQc cua nghi~m theo thalli sf{.<br /> A'<br /> <br /> §4.6. On d~nh mil trong kh6ng gian Banach.<br /> Lufjn wIn th[Jc Sf loan h{JC<br /> <br /> 50<br /> 52<br /> <br /> Mil nganh : 1.01.01<br /> <br /> 2<br /> Mlf ri)ng va ung d¥ng Btf di Gronwall-Bellman<br /> <br /> Hoang Thanh Long<br /> <br /> §4. 7. On dinh cae h~ tlfa di~u khi€n.<br /> ~<br /> <br /> §4.8. On dinh h~ kich dQngthu'ong xuyen.<br /> <br /> 56<br /> 59<br /> <br /> Ke't lu~n.<br /> <br /> 61<br /> <br /> Tfti li~u tham khao.<br /> <br /> 62<br /> <br /> 3<br /> Mi'Jri)ng va ling d~tngBd di Gronwall-Bellman<br /> ,<br /> <br /> Hoang Thanh Long<br /> <br /> ?<br /> <br /> L(J/ CAM (j N<br /> Ddu lien toi xin chan thanh cam an sau sdc den Thiiy<br /> PGS.TS. Nguy~n Dinh Phu:dii t(in tlnh huang ddn toi tit d~<br /> cuang den luc hoan thanh lu(in van.<br /> Toi xin chan thanh cam an haT Thiiy phiin<br /> <br /> bifn<br /> <br /> PGS.TS. Dinh Ngl)c Thanh va Thiiy TS. Nguy~n Thanh<br /> Long dii dQc lu(in van va dang gap nhi~u<br /> <br /> y kien<br /> <br /> quy bau.<br /> <br /> Toi xin chan thanh cam an cac Thdy Co TruiJng Dc;zi<br /> HQc Khoa HQc T1;C<br /> Nhien,<br /> <br /> TruiJng Dc;zi HQc Su Phc;zm,<br /> <br /> TruiJng Dc;zi HQc Bach Khoa dii t(in tlnh giang dC;Zy<br /> va<br /> <br /> truy~n dc;ztnhi~u kien thac mal, b6 ich giup tai lam quen<br /> ddn Val vi~c nghien cau khoa hQc.<br /> <br /> Tai ciing xin chan thanh cam an gia dlnh, cam an cac<br /> bc;zn luon luon df)ng vien, giup diJ va tc;zo<br /> dii<br /> di~u ki~n v~<br /> mQi m(it di tai hoan thanh to/t vi~c hQc.<br /> <br /> Luljn van tlUJC sl loan h{JC<br /> <br /> Mil nganh<br /> <br /> ..1.01.01<br /> <br /> 4<br /> MlJri)ng va u'ng d~tngBlf di Gronwall-Bellman<br /> <br /> Hoang Thanh Long<br /> <br /> DANH MUC KY HIEU<br /> .<br /> .<br /> <br /> Trang lu~n van nay co sa dl,mgcae ky hi~u va quy tide cgn thi€t.<br /> 1. IRll:Khong gian thl;icn chi~u.<br /> 2. IR+ = [0,00).<br /> 3. Q = [to,tr] c IR.<br /> <br /> 5. 1.1 Gia tfi tuy~t d6i .<br /> :<br /> 6. 11.11<br /> : Chu§'n. Tren IRllta lfiy chu§'n euclide.<br /> 7. exp(u) = ell.<br /> 8. Sup : C~n tren.<br /> 9. inf : C~n dtidi.<br /> 10. max : Gia tri IOn nhfit.<br /> <br /> 11. L : T6ng.<br /> 12. A<br /> <br /> = (aik),<br /> <br /> i,k<br /> <br /> = I,...,n,<br /> <br /> la ma tr~n vuong cfip n.<br /> <br /> n<br /> 13.<br /> <br /> IIAII<br /> <br /> = Sup I<br /> k<br /> i=l<br /> <br /> laik I,<br /> <br /> la chu§'n cua ma tr~n A.<br /> I<br /> <br /> 14. IIullL2=<br /> <br /> (1:,lu(xW dX)2 < 00.<br /> <br /> 15. Dam : Mi~n xac dinh.<br /> 16. Re : Phgn thl;ic.<br /> 17. (D) : K€t thlic chung minh.<br /> <br /> Lllqn van thl!c si loan h(JC<br /> <br /> Mil nganh : 1.01.01<br /> <br />