Stability of standing waves for logarithmic Schr\"odinger equation with attractive delta potential
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attractivedeltaequationlogarithmicodingerpotentialschrstability
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We consider the one-dimensional logarithmic Schr\"odinger equation with a delta potential. Global well-posedness is verified for the Cauchy problem in H1(R) and in an appropriate Orlicz space. In the attractive case, we prove orbital stability of the ground states via variational approach.
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