COMPUTATION FORMULAS OF GENERALIZED INVERSE PAD APPROXIMANTS USING FOR SOLUTION OF INTEGRAL EQUATIONS

ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅｇｅｎｅｒａｌｉｚｅｄｉｎｖｅｒｓｅｆｕｎｃｔｉｏｎ＿ｖａｌｕｅｄＰａｄ啨ａｐｐｒｏｘｉｍａｎｔｓｗａｓｉｎｔｒｏｄｕｃｅｄｔｏｓｏｌｖｅｉｎｔｅｇｒａｌｅｑｕａｔｉｏｎｓｉｎ [1 ] .Ｌｅｔｆ(ｘ ,λ)ｂｅａｇｉｖｅｎｐｏｗｅｒｓｅｒｉｅｓｗｉｔｈｆｕｎｃｔｉｏｎ＿ｖａｌｕｅｄｃｏｅｆｆｉｃｉｅｎｔｓ,ｉ.ｅ.,ｆ(ｘ ,λ) =ｃ0 (ｘ) ｃ1(ｘ)λ ｃ2 (ｘ)λ2 … ｃｎ(ｘ)λｎ … ,( 1 )ｗｈｅｒｅｃｊ(ｘ)ｉｓａｒｅａｌｏｒｃｏｍｐｌｅｘｆｕｎｃｔｉｏｎｗｉｔｈｒｅｇａｒｄｔｏ…     

THE POSITIVE SOLUTION OF CLASSICAL GELFAND MODEL WITH COEFFICIENT THAT CHANGE SIGN

ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅｎｏｎｌｉｎｅａｒｔｗｏ＿ｐｏｉｎｔｂｏｕｎｄａｒｙｖａｌｕｅｐｒｏｂｌｅｍ (ＢＶＰ)(Ｐ) ｗ″(ｔ) +λｈ(ｔ)ｅｗ(ｔ) =0 ,　　 0 ≤ｔ≤ 1 ,ｗ( 0 ) =ｗ( 1 ) =0(λ>0 )ｈａｓｂｅｅｎｐｒｏｐｏｓｅｄｂｙＧｅｌｆａｎｄ[1]ｗｉｔｈｈ(ｔ) ≡ 1 ,ｔｈｉｓｉｓｔｈｅｒｅａｓｏｎｗｈｙｗｅｓａｙｔｈｅｐｒｏｂｌｅｍ (Ｐ)ｉｓａＧｅｌｆａｎｄｍｏｄｅｌ.Ｓｅｍｉｌｉｎｅａｒｐｒｏｂｌｅｍｓｏｆｔｈｉｓｔｙｐｅａｒｉｓｅｉｎａｖａｒｉｅｔｙｏｆｉｎｔｅｒｅｓｔｉｎｇａｐｐｌｉｃａｔｉｏ…     

GLOBAL ATTRACTIVITY FOR A CLASS OF NONLINEARDELAY DIFFERENCE EQUATIONS

ＩｎｔｒｏｄｕｃｔｉｏｎＣｏｎｓｉｄｅｒｔｈｅｇｌｏｂａｌａｔｔｒａｃｔｉｖｉｔｙｏｆｔｈｅｎｏｎｌｉｎｅａｒｄｅｌａｙｄｉｆｆｅｒｅｎｃｅｅｑｕａｔｉｏｎΔｘｎ+ａｎｘｎ+ｆ(ｎ ,∑0ｓ=-ｋ ｑｓ,ｎｘｓ+ｎ) =0　 (ｎ=0 ,1 ,2 ,… ) . ( 1 )ＴｈｅｉｎｉｔｉａｌｖａｌｕｅｏｆＥｑ .( 1 )ｉｓｘｓ =φｓ　 (ｓ=-ｋ ,-ｋ+ 1 ,… ,-1 ,0 ) . ( 2 )Ｉｎｔｈｅｓｅｑｕｅｌ,ｗｅａｌｗａｙｓｓｕｐｐｏｓｅｔｈａｔＤ1) ａｎ ｉｓａｎｏｎｎｅｇａｔｉｖｅｒｅａｌｓｅｑｕｅｎｃｅ ,0 ≤ａｎ <1ａｎｄｋｉｓａｐｏｓｉｔｉｖｅ…     

A family of integrable systems of Liouville and lax representation,Darboux transformations for its constrained flows

ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅｗｅｌｌ＿ｋｎｏｗｎｂａｓｉｓｏｆｌｏｏｐａｌｇｅｂｒａ Ａ1ｉｓｔｈａｔｈ(ｎ) =λｎ 　 00 -λｎ ,　ｅ(ｎ) =0λｎ0 0 ,ｆ(ｎ) =0 0λｎ 0 ,[ｈ(ｍ) ,ｅ(ｎ) ] =2ｅ(ｍ+ｎ) ,[ｈ(ｍ) ,ｆ(ｎ) ] =　　 -2ｆ(ｍ+ｎ) ,[ｅ(ｍ) ,ｆ(ｎ) ] =ｈ(ｍ+ｎ) .( 1 )Ｍａｎｙｅｑｕａｔｉｏｎｈｉｅｒａｒｃｈｉｅｓｗｅｒｅｏｂｔａｉｎｅｄｂｙｅｓｔａｂｌｉｓｈｉｎｇｌｉｎｅａｒｉｓｏｓｐｅｃｔｒａｌｐｒｏｂｌｅｍｖｉａｔｈｅｕｓｅｏｆ( 1 ) ,ｓｕｃｈａｓＡＫＮＳｈｉｅｒａｒｃｈｙ ,ＫＮｈｉｅｒａ…     

On the existence of periodic solutions for nonlinear system with multiple delays

IntroductionInthispaper,westudyT_periodicsolutionsofthefollowingnonlinearsystemwithmultipledelays x(t) =f(t,x(t) ,x(t-τ1(t) ) ,… ,x(t -τm(t) ) ) ,(1 )wherex(t) ∈C(R ,R) ,fiscontinuous,f(t+T ,·) =f(t,·) ,τi(t) (i=1 ,2 ,… ,m)arecontinuousperiodicfunctionsofperiodT .AlemmaisintroducedfordiscussingtheexistenceofT_periodicsolutionofsystem (1 ) .LetXbeaBanachSpace ,considerthefollowingoperatorequation :Lx =λNx　　 (λ∈ [0 ,1 ] ) ,whereL :DomL∩X→Xisalinearoperator,λ∈ [0 ,1 ]isapa…     

一类非线性振动方程的渐近分析

本文用KBM方法处理非线性振动方程x+(a|x|~λ+bx|x|~μ+C)x+x=0,并且找到了该方程稳定周期解.最后,给出了软弹簧Rayleigh方程x+(a|x|~λ+bx|x|μ+c)x+(x-β~2x~3)=0的相应结果.     

BIFURCATIONS OF SUBHARMONIC SOLUTIONS IN PERIODIC PERTURBATION OF A HYPERBOLIC LIMIT CYCLE

Ｃｏｎｓｉｄｅｒｐｌａｎａｒｐｅｒｉｏｄｉｃｐｅｒｔｕｒｂｅｄｓｙｓｔｅｍ ｘ=ｆ(ｘ) +εｇ(ｔ,ｘ,ε ,δ) ,　　ｘ∈Ｒ2 ,( 1 )ｗｈｅｒｅε∈Ｒ ,δ∈Ｄ ＲｎｗｉｔｈＤｃｏｍｐａｃｔ,ａｎｄｆ,ｇａｒｅＣ3ｆｕｎｃｔｉｏｎｓａｎｄｇｉｓＴ＿ｐｅｒｉｏｄｉｃｉｎｔ,Ｔ >0 .Ｌｅｔｓｙｓｔｅｍ ( 1 )ｈａｓａｌｉｍｉｔｃｙｃｌｅＬ0 :ｘ =ｕ(ｔ) ,0 ≤ｔ≤Ｔ0 ｆｏｒε =0ｗｉｔｈＴ0 ｔｈｅｐｅｒｉｏｄｏｆＬ0 .ＳｕｐｐｏｓｅＴ0 /Ｔｉｓｒａｔｉｏｎａｌ,ｔｈａｔｉｓＴ0 /Ｔ=ｍ/ｋ,　　 (ｍ ,ｋ) =1 . ( 2 )Ａｓｗｅｋｎｏ…     

Difference scheme and numerical simulation based on mixed finite element method for natural convection problem

ntroductionLetΩ R2 beaboundeddomain .Weconsiderthefollowingnon_stationarynaturalconvectionproblem :Problem (Ⅰ )　Findu =(u1,u2 ) ,p ,andTsuchthat,foranyt1>0 ,ut- μΔu +(u· )u + p=λjT　　 ((x ,y ,t) ∈Ω× (0 ,t1) ) ,divu =0　　　　　　　　　 ((x ,y,t) ∈Ω× (0 ,t1) ) ,Tt-ΔT +λu· T =0　　 ((x,y,t) ∈Ω× (0 ,t1) ) ,u =0 ,T =0　　　　　　 ((x,y,t)∈ Ω× (0 ,t1) ) ,u(x ,y ,0 ) =0 ,　T(x,y,0 ) =f(x,y)　　 ((x,y) ∈Ω) ,whereuisthefluidvelocityvectorfield ,pthepressurefield ,Tthet…     

What are the separatrix values named by Leontovich on homoclinic bifurcation

Introduction LetVλ(x),x∈R2,λ∈RkbeafamilyofplanarC∞(oranalytic)vectorfields.Suppose thatforλ=λ0,Vλ0hasahyperbolicsaddlepointattheorigin(0,0)inthephaseplaneandthere isahomoclinicorbit(oraseparatrixloop)Γ0totheorigin.Thehyperbolicityratioattheorigin isr(λ)=-λ1/λ2,whereλ1<0<λ2arethetwoeigenvaluesofthelinearizedsystematthe origin.Generally,whenλ≠λ0and｜λ-λ0｜issmallenough,nearΓ0limitcycleswillbe created.Thisso_calledhomoclinicbifurcationhasbeenstudiedbyalotofauthors[1-3].Deno…     

A CLASS OF ALTERNATING GROUP METHOD OF BURGERS' EQUATION

IntroductionWeconsiderthefollowingnonlinearBurgers’equation : u t u u x=ε 2 u x2 ,　　 0 0 ,( 1 )withtheinitialandtheboundaryconditions　　　　　u(x,0 ) =f(x) ,　　 0 相似文献   

FIXED POINTS OF INCREASING OPERATORS IN ORDERED SPACE WITH APPLICATIONS

ＩｎｔｒｏｄｕｃｔｉｏｎＩｎｖｅｓｔｉｇａｔｉｎｇｔｈｅｆｏｌｌｏｗｉｎｇｂｏｕｎｄａｒｙｐｒｏｂｌｅｍｉｎｏｒｄｉｎａｒｙｄｉｆｆｅｒｅｎｔｉａｌｅｑｕａｔｉｏｎ :¨ｘ+ｆ(ｔ,ｘ(ｔ) ) =0 ,ａ<ｔ<ｂ,αｘ(ａ) -β ｘ(ａ) =0 ,γｘ(ｂ) +δ ｘ(ｂ) =0 ,( 1 )ｗｈｅｒｅα ,β,γ ,δ≥ 0 ,Δ=(ｂ-ａ)αγ+αδ+ βγ>0 .ｆ(ｔ,ｓ)ｍａｙｂｅｓｉｎｇｕｌａｒｉｎｔ =ａ ,ｂ.Ｉｔｈａｓｂｅｅｎｄｉｒｅｃｔｌｙｖｅｒｉｆｉｅｄｔｈａｔｘ(ｔ)ｉｓｔｈｅｓｏｌｕｔｉｏｎｏｆ( 1 )ｉｎＣ2 [ａ ,ｂ]ｉｆａｎｄｏｎｌｙｉｆｘ(…     

REMARK ON STABILITY OF ISHIKAWA ITERATIVE PROCEDURES

1　ＩｎｔｒｏｄｕｃｔｉｏｎａｎｄＰｒｅｌｉｍｉｎａｒｉｅｓＳｕｐｐｏｓｅＥｉｓａｒｅａｌＢａｎａｃｈｓｐａｃｅａｎｄＴｉｓａｓｅｌｆｍａｐｏｆＥ .Ｓｕｐｐｏｓｅｘ0 ∈Ｅａｎｄｘｎ+1=ｆ(Ｔ ,ｘｎ)ｄｅｆｉｎｅｓａｎｉｔｅｒａｔｉｏｎｐｒｏｃｅｄｕｒｅｗｈｉｃｈｙｉｅｌｄｓａｓｅｑｕｅｎｃｅｏｆｐｏｉｎｔｓ ｘｎ ∞ｎ=0 ｉｎＥ .Ｆｏｒａｎｅｘａｍｐｌｅ ,ｔｈｅｆｕｎｃｔｉｏｎｉｔｅｒａｔｉｏｎｘｎ+1=ｆ(Ｔ ,ｘｎ) =Ｔｘ0 .ＳｕｐｐｏｓｅＦ(Ｔ) =ｘ∈Ｅ :Ｔｘ=ｘ ≠ ａｎｄｔｈａｔ ｘｎ ｃｏｎｖｅｒｇｅｓｓ…     

ON NUMERICAL SOLUTIONS OF PERIODICALLY PERTURBED CONSERVATIVE SYSTEMS

ＩｎｔｒｏｄｕｃｔｉｏｎＣｏｎｓｉｄｅｒｔｈｅｐｅｒｉｏｄｉｃｂｏｕｎｄａｒｙｖａｌｕｅｐｒｏｂｌｅｍｏｆｔｈｅｏｒｄｉｎａｒｙｄｉｆｆｅｒｅｎｔｉａｌｅｑｕａｔｉｏｎｓＬｕ≡ｕ″(ｔ) +ｇｒａｄＧ(ｕ) =ｐ(ｔ) ,ｕ( 0 ) =ｕ( 2π) ,ｕ′( 0 ) =ｕ′( 2π) ,( 1 )ｗｈｅｒｅｐ∈Ｃ(Ｒ ,Ｒｎ) ,Ｇ ∈Ｃ2 (Ｒｎ,Ｒ) .ＴｈｅｅｑｕａｔｉｏｎｍａｙｂｅｉｎｔｅｒｐｒｅｔｅｄａｓｔｈｅＮｅｗｔｏｎｉａｎｅｑｕａｔｉｏｎｏｆｍｏｔｉｏｎｏｆｔｈｅｍｅｃｈａｎｉｃａｌｓｙｓｔｅｍｓｕｂｊｅｃｔｔｏｃｏｎｓｅｒｖａｔｉ…     

FIXED POINT THEOREM OF NONEXPANSIVE MAPPINGS IN CONVEX METRIC SPACES

Let X be a convex metric space with the property that every decreasing sequence ofnonempty closed subsets of X with diameters tending to(?)has nonempty intersection.This paper proved that if T is a mapping of a closed convex nonempty subset K of X intoitself satisfying the inequality:d(Tx,ty)≤ad(x.y) b{d(x,Tx) d(y,Ty} c{d(x,Ty) d(y,Tx)}for allλ.yin K,where0≤a<1,b≥0,c≥0,a c≠0 and a 2b 3c≤1,then T has auniquc fixed point in K.     

CONTROLLABILITY OF A CLASS OF HYBRID DYNAMIC SYSTEMS (Ⅱ)—SINGLE TIME_DELAY CASE

IntroductionConsideraswitchedlinearsystemwithsingletime_delayinthecontrolfunctiongivenby x(t) =Ar(t) x(t) +Br(t) u(t) +Dr(t) u(t -τ) ,(1)wherex(t) ∈Rnisthestate,u(t) ∈R mtheinput,thepiecewiseconstantscalarfunctionr(t) :R+ → 1,2 ,… ,Nistheswitchingpath ,(Ai,Bi,Di) ｜i =1,… ,Nisafinitefamilyofsystemrealizations.Moreover,r(t) =iimpliesthat(Ai,Bi,Di)ischosenasthesystemrealizationattimet.τ >0isthefixedtimedelayincontrol.Inthispaper ,wewillstudythecontrollabilityofsystem (1) .Theone_per…     

ON THE WELL POSEDNESS OF INITIAL VALUE PROBLEM FOR EULER EQUATIONS OF INCOMPRESSIBLE INVISCID FLUID (Ⅱ)

IntroductionForthestudyofwellposednessontheinitialorboundaryproblemsabouttheEulerequations,therearemanyimportantresultsgivenbydifferentmethodsindifferentfunctionclasses[1]- [4 ].Thepaper (Ⅰ )oftheauthordiscussedtheill_posednessoftheCauchyproblemswhichsatisfythesameconditionsoftheinitialvalueproblematthehypersurfacet=t( 0 ) +g(x) ,g(x) ≠constant,g(0 ) =0 R4,andgavetwodifferentformalsolutions[5 ].Italsogavetheformulasforcomputation .Inthepresentpaper,twokindsofillposednessoftheEulerequation…     

EXISTENCE OF POSITIVE RADIAL SOLUTIONS FOR SOME SEMILINEAR ELLIPTIC EQUATIONS IN ANNULUS

ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅｓｔｕｄｉｅｓｏｆｐｏｓｉｔｉｖｅｒａｄｉａｌｓｏｌｕｔｉｏｎｓｆｏｒｆｏｌｌｏｗｉｎｇｓｅｍｉｌｉｎｅａｒｅｌｌｉｐｔｉｃｂｏｕｎｄａｒｙｖａｌｕｅｐｒｏｂｌｅｍ(Ｐ)　Δｕ(Ｘ) +ｇ( ｜Ｘ｜)ｆ(ｕ(Ｘ) ) =0 ,　　Ｒ1<｜Ｘ｜<Ｒ2 ,ｕ(Ｘ) ｜｜Ｘ｜ =Ｒ1 =ｕ(Ｘ) ｜｜Ｘ｜ =Ｒ2 =0(ｗｈｅｒｅＲ1>0 ,Ｘ ∈Ｒｎ,ｎ ≥ 2 )ａｒｅｂｅｉｎｇｃｏｎｔｉｎｕｅｄｆｏｒｒｅｃｅｎｔ 2 0ｙｅａｒｓｗｉｔｈｏｕｔｉｎｔｅｒｒｕｐｔｉｏｎ[1- 11],ｂｅｃａｕｓｅｔｈｅｐｒｏｂｌｅｍ (Ｐ)ｈａｓｗｉ…     

CONTROLLABILITY OF A CLASS OF HYBRID DYNAMIC SYSTEMS (Ⅲ)—MULTIPLE TIME_DELAY CASE

IntroductionConsidertheswitchedlinearsystemwithmultipletime_delaysincontrolfunctiongivenby x(t) =Ar(t) x(t) +Br(t) u(t) + Kk=1Dr(t) ,ku(t -τk) ,(1)wherex(t) ,u(t)andr(t)isdefinedasbefore ,(Ai,Bi,Di,1,… ,Di,K)｜i=1,… ,Nisafinitefamilyofsystemrealizations.Moreover,r(t) =iimplies (Ai,Bi,Di,1,… ,Di,K)ischosenasthesystemrealizationattimet.K <∞isthenumberoftime_delaysinthesystem .0<τ1<… <τKareKfixedtime_delays .Remark 1　Similarly ,wecandescribeswitchingpathbyintroducingswitchingsequ…     

Boundedness and persistence and global asymptotic stability for a class of delay difference equations with higher order

ＩｎｔｒｏｄｕｃｔｉｏｎＣｏｎｓｉｄｅｒｔｈｅｆｏｌｌｏｗｉｎｇｄｅｌａｙｄｉｆｆｅｒｅｎｃｅｅｑｕａｔｉｏｎｗｉｔｈｈｉｇｈｅｒｏｒｄｅｒｘｎ+1=Ａ0ｘｐ0ｎ+ Ａ1ｘｐ1 ｎ- 1+… + Ａｋｘｐｋｎ-ｋ　　 (ｎ=0 ,1 ,2 ,… ) ,( 1 )ｗｈｅｒｅＡｉ,ｐｉ ∈ [0 ,∞ )　　 (ｉ=0 ,1 ,2 ,…ｋ;ｋ∈ 1 ,2 ,… ) ( 2 )ａｎｄｔｈｅｉｎｉｔｉａｌｃｏｎｄｉｔｉｏｎｓｘ-ｋ,ｘ-ｋ+1,… ,ｘ- 1,ｘ0 ａｒｅａｒｂｉｔｒａｒｙｐｏｓｉｔｉｖｅｎｕｍｂｅｒｓ.Ｓｏｍｅｓｐｅｃｉａｌｃａｓｅｓｏｆｋ=1ｆｏｒＥｑ .( 1 )ｈａｖｅｂｅｅｎ…     

Analysis of chebyshev pseudospectral method for multi-dimensional generalized srlw equations

IntroductionAsymmetricregularizedlongwaveequation (SRLWE) 2 x2 -1 u t = x ρ+ 12 u2 ,　 ρ t+ u x=0 (1 )hasbeeninvestigatedinRef.[1 ] .Thesystem (1 )ofequationsisshowntodescribeweaklynonlinearion_acousticwaveandspace_chargewaves.Thehuperbolicsecantsquaredsolitarywaves ,thefourconservationlaws,andsomenumericalresultshavebeenobtainedinRef.[1 ] .Obviously ,eliminatingρin (1 ) ,weobtainaclassofregularizedlongwaveequationutt-uxx+ 12 u2xt-uxxtt =0 . (2 )TheSRLWequationisexplicitlysymmetric…