非线性泛函微分方程解的性态

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100044)nsm(W)"&z
100081)ru(# a0j%j%{U
101114)kitT"G
B_qID;0f0HPjw;nZ[1]0-~&^UB_qID;::;7aL;:6&;G
1jhP[1–3]<HrJF

a(t)(y
(t))σ+q(t)f(y(t))=0,(1)1

2、Rh/{]v'G?}Jy1F?n7'

3、F(1)V[C1F


a(t)(y
(t))σ+q(t)fy(g(t))=0,(2)n


α−1

a(t)

4、y(t)

5、y(t)+q(t)fy(g(t))=0,(3)h/f9SF
1g1IQ!kxKNo[Pv;1.'><,F(3)1iW?

α−1

y(τ(t))β−1
a(t)

6、y(t)

7、y(t)+q(t)yτ(t)=01)[4,5]h'vh'?yF(3)169J6v1k^/,[1]

8、T[1]1d/]1o[su+=vr90<σ=p/q,ps5]qs<]αsE*,1<]q(t)≥0
>dsa(t)sPF<`]tlim→∞g(t)=∞>g(t)≥0;f(OG

9、
(u)≥0.D(i)uf(u)>0(u=0);(ii)fu1998410219FV-200245231FV-OR∗qNCj(19871005b)KI/2:7,X2G
B_qID;0f367w*SH9@`]y(t)sF(2)(i(3))1S
TAy(t)(OS(2)(iS(3)).9S
y(t)TAe5.?[t0,∞)K)9>27

10、msxmL6sO5BvEr9d)`]529.0CL,D9SkxgJH'G

11、Wa1N∞q(t)dt=∞,(4)6F(2)E)
y(t)i+8A,,>,
σ

σ(i),y(t)>0Pa(t)(y(t))≤0>a(t)(y(t))≥0;(ii),y(t)<0P

(t))σ)
≥0
σ

a(t)(y>a(t)(y(t

12、))≥0.'>$9@?y(t)≡0p1(5y(t)s
(t)>0;(ii)y(t)<0
1?&B $(i)y(t)<0>y>y(t)<0;(iii)y(t)>0

>y(t)>0;(iv)y(t)>0>y(t)<0,2Et≥t0.(F(2)/d3S

a(t)(y
(t))σ
a(t)(y
(t))σf
y(g(t))y
g(t)g
(t)
=−q(t)−
.(6)fy(g(t))f2y(g(t))Jh'KY_G??(i)Ilimy(t)=0,6=ID6∃M>0nt1≥t0,R/,t≥t1P
t→∞
y(

13、t)≤−M,yg(t)≤−M.(f1D)fy(g(t))≤f(−M)<0.&

σ
a(t)y(t)
≤−q(t),(7)fy(g(t))KS't1.tlJ)
σ
σtta(t)(y(t))a(t1)(y(t1))≤−q(s)ds≤−q(s)ds,(8)f(y(g(t)))f(y(g(t1)))t1t1'>
σ
tta(t)y
(t)≥−fy(g(t))q(s)ds≥−f(−M)q(s)ds,t1t1>
1/σ1t1/σy
(t)≥−f(−M)q(s)ds,a(t)t1lJ/
1/σt1s1/σy(t)≥y(t1

14、)+−f(−M)q(τ)dτds,(9)t1a(t)t1(S(5)>S(9)1*ct→∞>A,x@*-QsM])=368$Z25
?(ii)(rN
/∃M>0nt1≥t0,R/,t≥t1Py(t)≤−M,yg(t)≤−M.'>(f1D>fy(g(t))≤f(−M)<0,&(F(2)/

a(t)(y
(t))σ+q(t)f(−M)≥0,(10)KS't1.tlJ)tt

σ

σa(t)y(t)≥a(t1)y(t1)−f(−M)q(s)ds≥−f(−M)q(s)ds,t1t1>
1/σ1t1/σy
(t)≤−−f(

15、−M)q(s)ds,a(t)t1lJ/
1/