Nonexistence of positive vector solutions for quasilinear Schr¨odinger systems with vanishing potentials at infinity
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Abstract
We study a class of quasilinear Schr\"odinger systems arising in nonlinear optics, plasma physics, and Bose--Einstein condensates, in which the quasilinear term $\Delta(u^2)u$ induces density-dependent dispersion. Combining a change-of-variables technique for scalar quasilinear equations with the spherical-average method for elliptic systems, we prove that a nonexistence result for positive vector supersolutions of the corresponding semilinear system extends, under the same decay assumptions on the potentials, to the quasilinear system.
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References
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