Global existence for a coupled system of Schrödinger equations with power-type nonlinearities

نویسندگان

  • Nghiem V. Nguyen
  • Rushun Tian
  • Bernard Deconinck
  • Natalie Sheils
چکیده

u j : RN ×R → C, ψ j0 : RN → C for j = 1, 2, . . . , m and ajk = akj are positive real numbers. Global existence for the Cauchy problem is established for a certain range of p. A sharp form of a vector-valued Gagliardo-Nirenberg inequality is deduced, which yields the minimal embedding constant for the inequality. Using this minimal embedding constant, global existence for small initial data is shown for the critical case p = 1 + 2/N. Finite-time blow-up, as well as stability of solutions in the critical case, is discussed. C © 2013 American Institute of Physics. [http://dx.doi.org/10.1063/1.4774149]

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Global Existence for a Coupled System of Schrödinger Equations with Power-Type Nonlinearties Global Existence for a Coupled System of Schrödinger Equations with Power-Type Nonlinearties

In this manuscript, we consider the Cauchy problem for a Schrödinger system with power-type nonlinearities  i ∂ ∂tuj +4uj + ∑m k=1 ajk|uk||uj|uj = 0, uj(x, 0) = ψj0(x), where uj : R × R → C, ψj0 : R → C for j = 1, 2, . . . ,m and ajk = akj are positive real numbers. Global existence for the Cauchy problem is established for a certain range of p. A sharp form of a vector-valued Gagliardo-Niren...

متن کامل

Iterative scheme to a coupled system of highly nonlinear fractional order differential equations

In this article, we investigate sufficient conditions for existence of maximal and minimal solutions to a coupled system of highly nonlinear differential equations of fractional order with mixed type boundary conditions. To achieve this goal, we apply monotone iterative technique together with the method of upper and lower solutions. Also an error estimation is given to check the accuracy of th...

متن کامل

A Note on Coupled Nonlinear Schrödinger Systems under the Effect of General Nonlinearities

We prove the existence of radially symmetric ground–states for the system of Nonlinear Schrödinger equations

متن کامل

Spatial Disorder Of Coupled Discrete Nonlinear Schrödinger Equations

In this paper, we study the spatial disorder of coupled discrete nonlinear Schrödinger (CDNLS) equations with piecewise-monotone nonlinearities. By the construction of horseshoes, we show that the CDNLS equation possesses a hyperbolic invariant Cantor set on which it is topological conjugate to the full shift on N symbols. The CDNLS equation exhibits spatial disorder, resulting from the strong ...

متن کامل

Existence and multiplicity of nontrivial solutions for‎ ‎$p$-Laplacian system with nonlinearities of concave-convex type and‎ ‎sign-changing weight functions

This paper is concerned with the existence of multiple positive‎ ‎solutions for a quasilinear elliptic system involving concave-convex‎ ‎nonlinearities‎ ‎and sign-changing weight functions‎. ‎With the help of the Nehari manifold and Palais-Smale condition‎, ‎we prove that the system has at least two nontrivial positive‎ ‎solutions‎, ‎when the pair of parameters $(lambda,mu)$ belongs to a c...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2013