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


Authors: E. M. Harrell and B. Simon
Journal: Proc. Amer. Math. Soc. 88 (1983), 376-377
MSC: Primary 35J60
DOI: https://doi.org/10.1090/S0002-9939-1983-0695279-5
MathSciNet review: 695279
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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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DOI: https://doi.org/10.1090/S0002-9939-1983-0695279-5
Article copyright: © Copyright 1983 American Mathematical Society

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