一维P-Laplacian方程正解的三解定理

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1、263FAn((Vol.26No.32003A7PACTAMATHEMATICAEAPPLICATAESINICAJuly,2003∗P–Laplacian}
$'%(jg)Oo)J;)+O100080)#&"(&c0)=Co)100081)B%*FP-Laplaciansu9T#bz(ϕ(u
))
+a(t)f(u)=0,αϕ(u(0))−βϕ(u
(0))=0,γϕ(u(1))+δϕ(u
(1))=09/U#

2、Hp−2s,p>1.iϕ(s):=

3、s

4、8*.Zze]/UYa9*V}~P-Laplacianay[qLeggett-WilliamsD=A$12TP-Laplacian` x

ϕ(u
)+a(t)f(u)=0,0

5、s

6、s,P>1.Pw`(A)α>0,β≥0,γ>0,δ≥0;
(B)f∈C[0,∞),[0,∞);
(C)a∈C[0,1],[0

7、,∞)Ka(t)T(0,1)7RotM}Zq0eHQ'(1)T4xDirichlet`

8、
u(0)=0=u(1)_Z7.T"
2E[2,3]/h
";[1–5]vem-f~ic?Leray-SchauderS"Vv[3]ZQN)71997@
KT[1]hv3-Q'(1)T4x`

9、


u(0)−Bu
(0)=0,u(1)+Bu
(1)=0,(3)02bZ7.T"GhBi(v),i=0,1,FfS7Ikl
K.T#lm>0c6f(u)Bi(v)≤mv,IHuEv≥0,i=0,si=1&)

10、Tff$"
wf0=limup−1=x→0+0,f=limf(u)=+∞[1]∞x→∞up−1m,"
wf0=+∞,f∞=0,kL_
Wang'?Z7"mKransnoselskiiC<@#
)-x(1),(3).TZ7)U

11、
2001B4Q20Sh5∗gzvQ)u(19871005)nL!e?ou(1999000722)sn=3Fp*;_]0P-LaplacianR([8XA$505y
tEm^T[4]hv3-Q'(1)T4x`

12、
αu(0)−βu
(0)=0,γu(1)

13、+δu
(1)=0(4)bZ7.T"N-ff$"m,"7f
m-QNf9?pC

14、
(4)f(2)7wjL7QNH3Z
7'?kl7"gvLeggett-WilliamsC<@#
)-(1),(2).TdW`Z7)U

15、
"
Y`C<@#2?"]:Lm#UQ'` xW7.T"
(T[6–8].2?+QNv3` x(1),(2)Z7.T"
J[;4Roh2{7 ^/p
#37t[Cmyl
$kp7@62.1`E=E,·f

16、/`Banach!}
P⊂ES!
K4x(i)αu+βv∈P,I∀u,v∈P,α,β≥0&)
(ii)Th−u,u∈P,Eu=0,W%PfEh/`p2.2%>_ψf/`pPZ7SY+%Pk
Th4xψ:P→[0,∞)f+%7K
ψtu+(1−t)v≥tψ(u)+(1−t)ψ(v)IH∀u,v∈Pm0≤t≤1&)DpPvPkψ7@6
78U97yl100.@6Pr=u∈Pu

17、liamsC<@#,Yfm-h7#31[6−8]2.1`T:Pc→PcfP+%7KψfPZ7SY+%Pk
4xψ(u)≤u,∀u∈Pc.G`.T#l0

18、
&)(C1)u∈P(ψ,b,d)ψ(u)>b=∅,Kψ(Tu)>b,IH∀u∈P(ψ,b,d);(C2)Tub,IHu∈P(ψ,b,c)KTu>d.>5Td.TW`CaKψ(u3)

19、(C)^
.T#lη∈(0,2c61−η0

20、v

21、sgnvfϕ7OklQ
yβ111L=minL