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Using the methods in \\cite{Cazenave2} and analyzing the interaction between the nonlinearity $\\lambda_1|u|^{p_1}u$ and $\\lambda_2|u|^{p_2}u$, we not only partly solve the open problems of Terence Tao, Moni"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1009.0325","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-09-02T04:17:54Z","cross_cats_sorted":[],"title_canon_sha256":"7251609b1cd8b75460a493afe073e4cc2fadcf52ae59952752c6d2cd8eb1a641","abstract_canon_sha256":"7db13b000a6e439e275e4501b176abbe3b91c75d5f0e0720414cc03d58e34922"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:22:06.561355Z","signature_b64":"N1uXJStu2TjAIXMke+gl+dfsvHq4zrtKrY8OfbNlIliewfhNZZwxffL2DWhnng+j+pe0uJP7M0NMm43CnKVLBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cd349943341738cd5176d088b5fbcd8170b31857771e2d71317b9f090279382e","last_reissued_at":"2026-05-18T03:22:06.560576Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:22:06.560576Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Remarks on Scattering Properties of the Solution to a Nonlinear Schr\\\"{o}dinger Equation with Combined Power-Type Nonlinearities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Xianfa Song","submitted_at":"2010-09-02T04:17:54Z","abstract_excerpt":"In this paper, we consider the Cauchy problem of Nonlinear Schr\\\"{o}dinger equation \\begin{align*} \\left\\{\\begin{array}{ll}&i u_t+\\Delta u=\\lambda_1|u|^{p_1}u+\\lambda_2|u|^{p_2}u, \\quad t\\in\\mathbb{R}, \\quad x\\in\\mathbb{R}^N\n &u(0,x)=\\varphi(x), \\quad x\\in\\mathbb{R}^N, \\end{array} \\right. \\end{align*} where $N\\geq 3$, $0<p_1<p_2<\\frac{4}{N-2}$, $\\lambda_1$ and $\\lambda_2$ are real constants. 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