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arXiv · 1104.2684

Some Results on the Scattering Theory for a Schr\"{o}dinger Equation with Combined Power-Type Nonlinearities

Xianfa Song
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Abstract

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 $N\geq 3$, $0 0$ and $\frac{2}{N}<p<\alpha_0$ with $\alpha_0=\frac{2-N+\sqrt{N^2+12N+4}}{2N}$, which is also an open problem in this direction.

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Xianfa Song. 2011-04-14. Some Results on the Scattering Theory for a Schr\"{o}dinger Equation with Combined Power-Type Nonlinearities. https://arxiv.org/abs/1104.2684

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