λ-有理sturm-liouville问题谱

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©•nÙ.31˜Ù¥,·‚ÏLa'²;Sturm-Liouville¯K,é2ÂSturm-Liouville•§(!(t;z)u0)0+qu=zu;z2C;c1(t)2c2(t)2Ù¥p,q,c1,c2,r1,r2•[0;1)þ¢Š¼ê,!(t;z)=p(t)+zr1(t)+zr2(t);z2S2Cnfi=1fri(t):

6、t2(0;1)gg;p(t)>0;t2(0;1);r1(t)

7、t)ê,Xê¼ê÷vÛÜŒÈ^‡,Ï~¡•Hain-L•ust•§,ù˜a•§3A^êÆ+•äk2•A^[1320].ÏLa'²;Sturm-Liouville¯KéÙ?14•:!4•©a,34•:œ/e,‰Ñؘ‡¤kTitchmarsh-WeylXêáuKacaNevanlinna¼ê^‡.,,l†ƒƒA‡©•§XÚÝéuTitchmarsh-WeylXê±ã.i•H“‰ŒÆa¬ÆØ©31nÙ¥·‚•ÄSturm-Liouville¯K[2126]00qy+(p+)y=0;x2[0;1];u÷v>.^‡

8、y(0)=0;y(1)=0:ÄkéÙAŠ,cÙiAŠ?1O,U‰ÑiAŠØ•3^‡.'…c:=£Û:;Sturm-LiouvilleŽf;Titchmarsh-WeylXê;4•:/4•;Kaca;é¡Žf;gŠòÿ;knAŠ¯K;iAŠ.ii•H“‰ŒÆa¬ÆØ©AbstractTheSturm-Liouvilleproblemsarederivedfrommanymathematicalmodel-s,suchassolidheatconduction.At1910,H.WeylextendedtheStu

9、rm-Liouvilleproblemstounboundedintervals,therebycreatedthesingularSturm-Liouvilletheory.Afterthat,Weyltheorybecomesanimporta