关于微分方程解的唯一性

(

100080;

100049)

DS

SV(D)Klostermeyer

D

S,

DD,

D,D

V(D)

(X,Y),

|Y|

NP−

3≤|X|≤|Y|≤2|X|−1−1,2|X|−1−1

MR(2000)

05C20

1

D

D

,

.

u,v∈V(D),Du

vvuD;|V(D)|≥k+1(k≥1),

kV(D)U,D−UDk−.S⊆V(D),DS,DSDSDSS=φ,DS=D.D,S⊆V(D),DSD.

Mosesian[1]Pretezel[2]Klostermeyer[3]

D,S⊆V(D),DS

HamiltonNP−Huang,MacGillvrayYeo[4,5][7]

KlostermeyerSoltes[6],Liu

HamiltonKlostermeyerSoltes[8]k≥1,

nk,|V(D)|≥nkD,k−

D=(X,Y;A)

A=A(D),(X,Y)V(D)

V(D)A(D)

UG(D)D

D

D

D

UG(D)UG(D)

UG(D)

,S⊆V(D),DSHUG(H)=K2,󰀎,󰀂

|V(H)X|=2.

X={x1,x2,···,xn1},Y={y1,y2,···,yn2},n1=|X|,n2=|Y|.

󰀂

󰀢=2D1≤i≤n1,N+(xi){y1,y2}=φ,

󰀂

x∈X,N+(x){y1,y2}=φ,Dx

S⊆V(D),DSHUG(H)=K2,2.F1=D[{x1,x2,y1,y2}],

++

K2,2F1∼NF(x1)={y1,y2},NF(x2)={y1}.=B4,11

+

F2=D[{x2,x3,y1,y2}],F2∼NF(x3)={y1,y2}.F3=D[{x1,x3,y1,y2}],=B4,2

2

S1⊆V(D),D1=DS1F

󰀂+

UG(F)=K2,2,V(F)={x1,x2,y1,y2}.Y1={y∈Y:|ND(y){x1,x2}|=1},1

󰀁

|Y1|≥󰀢,Y󰀅⊆Y1,|Y󰀅|=󰀢{y1,y2}⊆Y󰀅,H=D1[V(F)Y󰀅]

󰀂+

|Y1|<󰀢,Y2={y∈Y\\Y1:ND(y){x1,x2}=φ},D2=(D1)Y2

1

2

,

y∈Y\\Y1,y

x1

x2.

y󰀅∈Y\\Y1,S2={x1,y󰀅},

|Y\\Y1|≥|Y|−(󰀢−1)≥

|Y|+1

2

,

UG(H)=K2,k,

󰀃|=2n−2−1,V(H).|Y

󰀄DD11

|Y|≥2|X|−1n,n󰀅n≥3n󰀅≥2n−1

Kn,n󰀁D=(X,Y;A)X={x1,x2,···,xn},Y={y1,y2,···,yn󰀁},nF={X󰀅⊆X:1≤|X󰀅|≤n−1

󰀁󰀅−1}{X⊆X:|X󰀅|=n2

x󰀅󰀅

2.1S⊆V(D),D1=DS

󰀂󰀅󰀅󰀄D|V(H)X|=2.D11=D1[H→x]󰀃Y󰀃)󰀄󰀃|=n−1,(X,V(D|X1)

H

H