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Sharp conditions of global existence for second‐order derivative nonlinear Schrödinger equations with combined power‐type nonlinearities
Author(s) -
Xu Runzhang,
Xu Chuang
Publication year - 2013
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.201200083
Subject(s) - nonlinear system , mathematics , type (biology) , derivative (finance) , invariant (physics) , class (philosophy) , mathematical analysis , order (exchange) , cauchy problem , power (physics) , initial value problem , mathematical physics , physics , quantum mechanics , computer science , ecology , finance , artificial intelligence , financial economics , economics , biology
We undertake a comprehensive study of the Cauchy problem of a class of second‐order derivative nonlinear Schrödinger equations with combined power‐type nonlinearities. Using the potential theory and the concavity method, we construct a variational problem and two invariant manifolds. Furthermore, we give sharp conditions of global existence and blowup.