Some Results on the Scattering Theory for a Schrödinger Equation with Combined Power-Type Nonlinearities

Details Some Results on the Scattering Theory for a Schrödinger Equation with Combined Power-Type Nonlinearities Some Results on the Scattering Theory for a Schrödinger Equation with Combined Power-Type Nonlinearities

2011-04-14

arxiv.org/abs/1104.2684v1

Mathematics

Analysis of PDEs

18 pages

Scientific paper

In this paper, we consider the Cauchy problem {align*} \{{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 &u(0,x)=\phi(x)\in \Sigma, \quad x\in\mathbb{R}^N, {array}. {align*} where $N\geq 3$, $00$ and $\frac{2}{N}

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