The paper establishes existence and multiplicity of L^2-normalized solutions for a biharmonic Schrödinger equation with mixed dispersion and Sobolev critical nonlinearity, in both mass-subcritical and mass-supercritical regimes.
Existence and instability of standing waves for the biharmonic nonlinear Schroedinger equation with combined nonlinearities
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abstract
We prove the existence of normalized ground state solutions for the biharmonic Schr\"odinger equation with combined nonlinearities and show that all ground states correspond to the local minima of the associated energy functional restricted to the appropriate set. Moreover, we prove that the standing waves are strongly unstable by blowup. In particular, our results cover the critical case. Our method is novel and innovative as previous ideas cannot be used in many cases under this study.
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Normalized solutions to focusing Sobolev critical biharmonic Schr\"{o}dinger equation with mixed dispersion
The paper establishes existence and multiplicity of L^2-normalized solutions for a biharmonic Schrödinger equation with mixed dispersion and Sobolev critical nonlinearity, in both mass-subcritical and mass-supercritical regimes.