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On the orbital stability of inhomogeneous nonlinear Schr\"{o}dinger equations with singular potential

조용근|Misung Lee
대한수학회 (The Korean Mathematical Society)|2019.11|대한수학회보 (Bulletin of the KMS)|제56권 제6호|pp. 1601-1615|DOI 10.4134/BKMS.b190029

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키워드

inhomogeneous NLSsingular potentialground stateorbital stabilitywell-posednessStrichartz solution
주제분류수학

초록

We show the existence of ground state and orbital stability of standing waves of nonlinear Schr\"{o}dinger equations with singular linear potential and essentially mass-subcritical power type nonlinearity. For this purpose we establish the existence of ground state in $H^1$. We do not assume symmetry or monotonicity. We also consider local and global well-posedness of Strichartz solutions of energy-subcritical equations. We improve the range of inhomogeneous coefficient in \cite{guz, din} slightly in 3 dimensions.

Abstract

We show the existence of ground state and orbital stability of standing waves of nonlinear Schr\"{o}dinger equations with singular linear potential and essentially mass-subcritical power type nonlinearity. For this purpose we establish the existence of ground state in $H^1$. We do not assume symmetry or monotonicity. We also consider local and global well-posedness of Strichartz solutions of energy-subcritical equations. We improve the range of inhomogeneous coefficient in \cite{guz, din} slightly in 3 dimensions.

참고문헌 (18)

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