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ඇઢܗ4DISÖEJOHFS 1PJTTPOํఔࣜͷ
 ఆৗ೾ղͷଘࡏͱඇଘࡏ ߴڮ࿨Ի ౦ژେֶେֶӃ਺ཧՊֶݚڀՊത࢜ޙظ՝ఔ೥

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͜ͷݚڀ͸ɼٶݪ߂ߦࢯͱͷ
 ڞಉݚڀͰ͢ɽ<.5> [MT] Hiroyuki Miyahara and Kazune Takahashi.
 Existence and nonexistence of standing wave solutions of nonlinear schrödinger- poisson system. preprint.

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j໰୊ɾઌߦݚڀɾ ओఆཧ

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˒ ໰୊ ͸ͷୈݻ༗஋ ׈Β͔ɼ༗քྖҬ ʹͷͱ͖ྟքɺʻͷͱ͖ྼྟքͱݺͿ

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͕ٿͷͱ͖ɼͳΒ͹ɼ ˒ ͸ඇࣗ໌ղΛ࣋ͭɽ ͕੕ܗͷͱ͖ɼͳΒ͹ɼ ˒ ͸ ඇࣗ໌ղΛ࣋ͨͳ͍ɽ ઌߦݚڀ ຆͲ͕ ଟ͕͘ྼྟք <"E> 5IFPSFN ͷ߲͸ͳ͍ ͸ྟք

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ͷΈͳΒͣ ྟքͷΈͳΒͣྟքͷέʔε΋ ͷΈͳΒͣ ˒ ઌߦݚڀͱͷൺֱ

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ओఆཧ ղ͕ଘࡏ͢Δे෼৚݅ʜ5IFPSFN 5IFPSFN 5IFPSFN 5IFPSFN ղ͕ଘࡏ͠ͳ͍े෼৚݅ʜ5IFPSFN ഑෍ࢿྉΛࢀর

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ղͷଘࡏɾඇଘࡏ͕ܾఆ͢Δྫ ղ͋Γ5IN W ੕ܗղͳ͠5IN J ੕ܗղͳ͠5IN ٿղ͋Γ5IN ࢀߟ<"E>

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jূ໌ͷϙΠϯτ

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ม෼๏ ͷྟք఺ʹର͠ɼ͸ ˒ ͷղɽ ͷ།Ұղɽ ͸ ͜͜Ͱ ΛҎԼͰఆΊΔɽ

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5IFPSFNͷϙΠϯτ ͷྟք఺ ಕͷิ୊ ಕͷิ୊ͷԾఆ J ɽ JJ ͕ଘࡏ͠ɼ೚ҙͷʹର͠ɼ
 JJJ ͕ଘࡏ͠ɼ


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J ɽ JJ ͕ଘࡏ͠ɼ೚ҙͷʹର͠ɼ
 JJJ ͕ଘࡏ͠ɼ
 ্͕ͳ͢໘

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5IFPSFNͷϙΠϯτ ͷྟք఺ ಕͷิ୊ ಕͷิ୊ͷԾఆ J ɽ JJ ͕ଘࡏ͠ɼ೚ҙͷʹର͠ɼ
 JJJ ͕ଘࡏ͠ɼ
 ͜ͷதͰ͸ JJJ ͕Ұ൪ݫ͍͠ˠ5IFPSFNͷ৚݅

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͸ɼ5IN J JJ JW ͷͱ͖ɼଈै͏ɽ 5IFPSFN

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5IFPSFN ͷͱ͖ Ͱܾ·Δɽ ͸ɼ

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5IFPSFN ͷͱ͖ -FNNB Ͱ໌ࣔతʹٻ·Δɽ ˠ5IN JJJ ˠ5IN W

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ಕͷิ୊ͷؼ݁ ࢁΛӽ͑Δ࠷খͷߴ͞ ͷ఺͕ྟք఺ ྟք఺ʹۙͮ͘఺ྻ͕ಘΒΕΔ ऴ఺

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ಕͷิ୊ͷؼ݁ ྻ͕ಘΒΕΔɽ ఆٛ ͕ྻͰ͋Δͱ͸ ఆٛ NPVOUBJOQBTTMFWFM ͜͜Ͱ͸ͱ೚ҙͷऴ఺Λͭͳ͙ಓɽ

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5IFPSFN ͷϙΠϯτ ͷྟք఺ ಕͷิ୊ ྻ͕ಘΒΕΔɽ ಕͷิ୊ͷؼ݁ ऑऩଋઌ͕ྟք఺Ͱ͋Δɽ ༰қ ྟքࢦ਺ 5IN ͷ৔߹ ΛಘΔͨΊʹɼ NPVOUBJOQBTTMFWFMʹ৚͕݅ͭ͘ɽ 5BMFOUJؔ਺Λ࢖͏<#/>

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5BMFOUJؔ਺ ࢖༻ํ๏ ࢁΛӽ͑Δಓͱͯ͠ํ޲ͷ൒௚ઢΛબͿɽ Λখ͘͞͠ɼΛධՁ͢Δɽ ͸্ͷDVUP⒎GVODUJPO

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5IFPSFN ͷख๏ 5INɿ<#/>ͷख๏ 5INɿ<"E>ͷख๏ʜʜ<#/>Λ޻෉͢Δɽ J JJ ͕ಘΒΕΔɽ JJJ W ͸͞Βʹ޻෉͢Δɽ

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5IFPSFN Λূ໌͍ͨ͠ɽഎཧ๏ɿͱԾఆ͢Δɽ ͕ྻͰ͋Δ͜ͱ͔Βɼ ࿈ཱํఔࣜղ͚Δ ͜ͷܭࢉ݁Ռͱɼ4PCPMFWෆ౳ࣜͳͲΑΓɼ ͕ඞཁɽʜ ̇ ͱ͓͘ɽ

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5IFPSFN ͷͷ߲ΛධՁ͢Δɽ ৗʹ͕੒ཱ͢Δɽ མͱ͢ 5IN J JJ ͷͱ͖͕੒ཱ͢Δɽ

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5IFPSFN J JJ ͜͜Ͱ͸ͷ།Ұͷਖ਼஋ղɽ ໌ࣔతʹॻ͚Δ

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5IFPSFN J JJ ͜͜Ͱ͸ͷ།Ұͷਖ਼஋ղɽ ໌ࣔతʹॻ͚Δ ܭࢉʹΑΓͱΘ͔Δɽ ͱ͓͘ͱɼ ̇ ʹໃ६ 5BMFOUJؔ਺ͷͷٞ࿦͔Β J JJ ͕ಘΒΕΔɽ

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͜͜Ͱ͸ͷ།Ұͷਖ਼஋ղɽ 5IFPSFN JJJ W 5IN JJJ W ͸ߋʹ޻෉ ໌ࣔతʹॻ͚ͳ͍

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͜͜Ͱ͸ͷ།Ұͷਖ਼஋ղɽ 5IFPSFN JJJ W ໌ࣔతʹॻ͚ͳ͍ ͱ͜Ζ͕ɼ ͸ͷʹӨڹΛ༩͑ͳ͍

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5IFPSFN JJJ W ͸ͷʹӨڹΛ༩͑ͳ͍ -FNNB JJJ W ͕ಘΒΕΔɽ

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˒ ղ͋Γ5IN W ੕ܗղͳ͠5IN J