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6.091900 2007. 1 .. ..., .. .. ..-.., . .. , .. ..., , - :,, . , . , ,. - . : 1. , , , , , . 2. , . . 3. , ,. 24. , . ,. 5.3 4.. 6. . . , . 7. ( , ), . . 8. . 9. , . 3 I.1.. . ' ) ,... , , (......... .......... .......... ..........,... , , () ,... , , (2 1) 2 1 2 22 1 1 1n n nnny y y x f yy y y x f yy y y x f y(I.1) ) ,... 1 ( n i fi ) 1 ( + n D ny y y x ,..., , ,2 1. ). ( ),..., ( ), (2 1x y x y x yn, ( I.1), . (I.1) ( ,b) ) ( ),..., ( ), (2 1x y x y x yn, ( ,b) ( I.1) . . ). ( ),..., ( ), (2 1x y x y x yn,: , ) ( ,..., ) ( , ) (0 0 20 0 2 10 0 1 n ny x y y x y y x y (I.2)0 20 10,... ,ny y y ; ) , (0b a x 4( ). ) ,..., 1 ( n i fi D y y xn ) ,..., (0 , 10 , 0 ) ,..., 1 ( n jyfji, 0x , ( I.1),. (I.1) n ) ,.. 1 ( ) ,..., , , (2 1n i C C C x yn i i , n nC C C ,...,2 , 1: 1) i nC C C x ,..., , ,2 1 ;xi2)i( I.1) iC.3) ( I.2) D, , 0 20 10,..., ,nC C C , ) ,..., , , (0 20 10 0 0 n iC C C x y n. (I.1), . ( I.1) ( ). , 5) ( ) ( ... ) ( ) (....... .......... .......... .......... .......... .......... .......... .......... ..........) ( ) ( ... ) ( ) () ( ) ( ... ) ( ) (2 2 1 12 2 2 22 1 21 21 1 2 12 1 11 1x f y x a y x a y x a yx f y x a y x a y x a yx f y x a y x a y x a yn n nn n n nn nn n+ + + + + + + + + + + + (I.3) ) ,..., 1 ( ), ( n i x fi ). ; ( b a 0 ) ( x fi, , . const, ) ( x aij . ., 0........ .......... .......... ................2 12 22 211 12 11nn n nnna a aa a aa a a,. const ija, n , , , n . . 1. . . 2 1,..., ,n , ) ,.., 1 ( n ii , ,..., ,) ( ) ( ) (2) (2) (1) (1x ininx i i x i ii i ie y e y e y (I.4)6 ) ( ) (2) (1,..., ,ini i ' + + + + + + + + + 0 ) ( ............. .......... .......... .......... .......... .......... ..........0 ... ) (0 ... ) () ( ) (22) (11) (2) (222) (121) (1) (212) (111in nnininin ni iin ni ia a aa a aa a a . (I.5)( I.4) . , ( I.3) const ) ( x aij,0 ) ( x fi, , ( I.4):'+ + + + + + + + + x nn nx n x nniin i nx nnx xniiix nnx xniiinnnC C C y C yC C C y C yC C C y C y e ... e e.... .......... .......... .......... .......... .......... .......... .......... .......... .......... ..........e ... e ee ... e e) ( ) (22) (111) () (2) 2 (22) 2 (111) (22) (1) 2 (12) 1 (111) (112 12 12 1 iC . 2. n ,..., ,2 1 , ., - i t 2 , 1 : ( )( ). e, e) 2 ( ) 2 () 1 ( ) 1 (x ij jx ij jyy +(I.6)7 n j ,..., 1 ;) 2 ( ) 1 (,j j ( I.5) i + 1 i 2. ) 2 ( ) 1 (,j j , , , ) 2 ( ) 1 (,j jy y . ) 1 (jy ) 2 (jy , , , , . 3. n ,..., ,2 1 . k . ( I.2) ( const ija, 0 ) ( x fi( ) ,..., 1 , n j i ), k , : ( )( )( ) . e ............. .......... .......... .......... .......... .......... .......... ..........e ...e ...11 ,22 1 011 , 2222 21 20 211 , 1212 11 10 1x kk n n n n nx kkx kkx x x yx x x yx x x y + + + + + + + + + + + + (I.7)( ) 1 ,..., 1 , 0 ; ,..., 1 k j n iij : iy ( I.7) (3) ija) (x if, , x e, x . ijk, . , ( ) , ,. . 1 2. 8I.2. , , ( I.7) , . nC C C ,..., ,2 1 ( I.7)., ( I.7), nC C C ,..., ,2 1 ) ( ),..., ( ), (2 1x C x C x Cn( nC C C ,..., ,2 1). : ny y y ,..., ,2 1 ny y y ,..., ,2 1, n ) ( ),..., ( ), (2 1x C x C x Cn , ) ( ) ( ),..., ( ) ( ), ( ) (2 2 1 1x x C x x C x x Cn n , ) ,..., 1 ( ) ( n i xi . , : i i iC dx x x C ) ( ) ( , iC . ( I.7) const iC ) (x Ci, . I.3. , , 1y , ) (1x y 9 (( I.3) const ija) n ., ) ( ),..., (2x y x yn . , x ( I.3) ( const ija), ny y y ,..., ,2 1 ( I.3).: ) ( ) ,..., ( ) ( ...2 1 2 1 1 2 12 1 11 1x F y y L x f y a y a y a yn n n+ + + + + ,(I.8) ) ,..., (1 2 ny y L ny y y ,..., ,2 1, ) (2x F ) ( ),..., ( ), (2 1x f x f x fn ) (1x f . (I.8)x , ) ( ) ,..., (3 1 3 1x F y y L yn+ ., ) ( ) ,..., (1) (1x F y y L yn n nn+ n : '+ + + + + + + ) ( ) ,..., , () ( ) ,..., , (. .......... .......... .......... .......... .......... ..........) ( ) ,... , () ( ...2 1) (11 2 1 1) 1 (12 2 1 2 11 1 2 12 1 11 1x F y y y L yx F y y y L yx F y y y L yx f y a y a y a yn n nnn n nnnn n(I.9)10 1 n ( I.9) ) ( ),..., (2x y x yn( , , ). , ) 1 (11 1,..., , ,ny y y x:( )( )( )) 1 (1 1 1) 1 (1 1 1 3 3) 1 (1 1 1 2 2,..., , ,... .......... .......... .......... ..........,..., , ,,..., , , nn nnny y y x yy y y x yy y y x y (I.10) ) ( ),..., (2x y x yn ( I.10) ( I.9), n ( )) 1 (11 1) (1,..., , , n ny y y x F y,,: ( )nC C x y ,.., ,1 1 1 . (I.11), 1 n x , ) 1 (11 1,..., , ny y y, ( I.10) (I.11): ( )( )( )n n nnnC C x yC C x yC C x y,..., ,... .......... .......... ..........,..., ,,.., ,11 3 31 2 2(I.12)11( I.11)(I.12) nC C ,...,1 ( I.11)( I.12).II. ,. , - , , , . , . , , ,,, . n i y y tdtdyn ii,..., 1 ), ,..., , (1 (II.1) ( ) ) ,..., 1 (0 0n i y t yi i , , , , . , , , , ,. 12II.1. , , . II.1.1. ( II.1) 1 + nRny y t ,..., ,1, ( II.1) ,. nRny y ,...,1 , . , ( II.1): 1. ,; 2.( ); 3.. : n i y ydtdyn ii,..., 1 ), ,..., (1 (II.2)., , t .13II.2. ( II.2). , , ( II.1). , , ,, 1 . , , ( )0 10,...,ny y M ( II.2),: n i y ydtdyn ii,..., 1 , 0 ) ,..., (0 10 . (II.3)( II.3) , , ( ): ' 0 ) ,..., (........ .......... ..........0 ) ,..., (0 ) ,..., (11 21 1n nnny yy yy y. (II.4),: '+ + + + + + + + + , ............ .......... .......... .......... ................2 2 1 12 2 22 1 21 21 2 12 1 11 1n nn n n nn nn ny a y a y a yy a y a y a yy a y a y a y (II.5)( ) . 1 .14,: n idtdyyii,..., 1 , ., ), , ( ), , ( y x Qdtdyy y x Pdtdx ) , ( y x P ) , ( y x Q x y, ) , (* *y x M , ( ) 0 ,* * y x P , ( ) 0 ,* * y x Q . , ., y a x a y y a x a x22 21 12 11, + + 022 2112 11a aa a.: 1. : 2 1 2 1, , R 02 1> ( ), ( ). 1 );152. : 2 1 2 1, , R 02 1< ( ), ( . 1 ));3. , ( , ). 1 );4. ( ), ( . 1 );5. , ( . 1 );6. , ( : 021 12 22 11 a a a a ), xOy. ( , xOy ), , , , , , ( ). , . : , ( ). 16. 1. .

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nn n nnna a aa a aa a a...... ... ... .........2 12 22 211 12 11A ,,, h( ) .: h Ah . (II.6) h, .. ( II.6), 0 h Ah h Ah .: ( ) 0 h E A , ( E), , . : ( ) 0 det E A (II.7),. ( II.7): 170...... ... ... .........2 12 22 211 12 11nn n nnna a aa a aa a a. (II.8),, ( II.8),, , n :) ,..., 0 ( const , ... ) (11 0n i c c c c Pi nn nn + + + . (II.9),,, ( II.9) n, . , A n ( ).. , , , ( , ),. . , , . . , ,,, . -

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dtdydtdx, . II.1.3. 18 0 ix ) ,..., 1 ( n i ), ,..., 2 , 1 ( ) ,..., , , (2n i x x x t fdtdxn i ii (II.10)if , . ) ,..., , , (2 1 n ix x x t f , ( II.10) 0 ix ) ,..., 1 ( n i ) ,..., 2 , 1 ( ) ,..., , , ( ) (2 11n i x x x t R x t adtdxn injj iji + , (II.11)iR niix12, 0 ix ) ,..., 1 ( n i ( II.10) , ) ,..., 2 , 1 ( ) ( n i x t adtdxj iji ,(II.12) ( II.11)., , , . 1. (II.11) , iR t T t 0 +

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2112nii ix N R,N const , 190 > ( . ., iR t , : niix x12 0.......... .......... .......... ................2 12 22 211 12 11nn n nnna a aa a aa a a,(II.13) , () 0 ix ) ,..., 1 ( n i (II.11) (II.12) . 2. (II.11) , iR , (II.13) , 0 ix ) ,..., 1 ( n i (II.11) (II.12). 1. 0 , 0 y x' + + + ., sin22 2y y xdtdyt y x y xdtdx 1 2. 0 , 0 y x : 20'+ y xdtdyy xdtdx 01 11 1 i t 12 , 1 . , 2, . 2. 0 , 0 y x' + y y edtdyy xdtdxxcos 3 2sin 8 2. , sin yy cosxe, '+ + + 2138 2R y xdtdyR y xdtdx, 1R 2R1 2. : 2103 18 2 . . , ,, 0 , 0 y x . II.2. ,, , ,. , ) , ( x t V V , , ) ,..., , ( ) , (11n iniix x t gxVtVdtdVx t V + ,( II.1), ( ) ,..., , (1 n ix x t g ). , . . . ( . . ). ,,, V, V () V, ,. , 220) 1 . (IIdtdV0 0, t t x > < : 0 ) () 1 . (II< x WdtdV0 0, 0 t t x > < < , ) (x W 0 < x , ( II.1) . ( . .). (II.1). nx x ,...,1 ) ,..., (1 nx x V , :1. 0 x ;2. 0 V 0 < x ;3. 0t t > 0 > V ,0 ) () 1 . (II> x WdtdV, ) (x W. (II.1). V , ( II.1). ninjj i ijx x b x V1 1) (, st con ijb, . 23II.3. 1). 0 , 0 ...0 111 0> + + + +a a a a an nn n , (II.14). ).: 0 >ia . 2 n . ). : ,

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naa a a a a aa a a aa a... 0 0 0 0 0 0... ... ... ... ... ... ... ...0 ...0 ... 0 00 ... 0 0 0 00 1 2 3 4 50 1 2 30 1. na a a ,..., ,2 1. . ia n i > 0 < i. ,...0, ,3