几类非线性脉冲方程的解及其应用.pdf

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2、ECouDWeW
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3、3WeW<W3/q+5ZlkVu<V[b

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l4(p(t)u′(t))′+m(t)f(t,u(t),u′(t),(Tu)(t),(Su)(t))=θ,∀t∈J′,△u

5、t=tk=−Ik(u(tk),△(p(t)u′(t))

6、

7、=−I(u(t),u′(t)),k=1,2,···,m,t=tkkkkαu(0)−βp(0)u′(0)=θ,′γu(1)+δp(1)u(1)=θ,′!ÆJ=[0,1),00,f∈C(J×E×E×E×E,E),Ik∈C(E,E),Ik∈C(E×E,E),m∈C(J,[0,+∞)),p∈RC(J,(0,+∞))∩C1[0,+∞),ρ=βγ+αδ+αγB(0,1)>0,s1xvB(t,s)=tp(r)dr.RRt1(Tu)(t)=k(t,s)u(s)ds

8、,(Su)(t)=h(t,s)u(s)ds.l
WBanachl=00x[?1>n'`℄_uVSvWW
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9、^ÆW$
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10、=−I(u(t)),k=1,2,···,n,t=tkkkZ+∞αu(0)−βp(0)u′(0)=h(s)u(s)ds,0

11、Z+∞′γlimu(t)+δlimp(t)u(t)=g(s)u(s)ds,t→+∞t→+∞0′!ÆJ=[0,+∞),00,ρ=βγ+αδ+αγB(0,+∞)>0.V[Leggett-tp(r)Williams'`℄_uVSvG^zW
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12、^ÆWl[qÆs
tBan

13、achl=Æn−
w4)0Æ<z−.zt6x(n)=f(t,x,x′,···,x(n−1),Tx,Sx),t∈J,t6=t,k∆x(i)

14、=I(x(t),x′(t),···,x(n−1)(t)),k=1,2,···,m,t=tkikkkkx(i)(0)=x,i=0,1,···,n−1,i(i)(i)+(i)−(i)+(i)−(i)!Æ∆x

15、t=tk=x(tk)−x(tk),!Æx(tk)x(tk)z$#Vx(t)lt=tkCW!_0xvZtZa(Tx)(t)=k(t,s)x(s)ds,(Sx)(t)=h(t,s)x(s)d

16、s,00k∈C[D,R+],h∈C[J×J,R+],R+=[0,+∞),D={(t,s)∈J×J

17、t≥s}.