Schrödinger operator methods in the study of a certain nonlinear P.D.E

Harrell, E. M.; Simon, B.

doi:10.1090/S0002-9939-1983-0695279-5

Schrödinger operator methods in the study of a certain nonlinear P.D.E
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by E. M. Harrell and B. Simon

Proc. Amer. Math. Soc. 88 (1983), 376-377

DOI: https://doi.org/10.1090/S0002-9939-1983-0695279-5

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Abstract:

We prove that $\Delta u + h{u^\alpha } = 0$ has no positive solutions for certain $h$, $\alpha$ by studying the linearized equation $(\Delta + h{u^{\alpha - 1}})\psi = e\psi$.

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