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Positive solutions to elliptic equations in unbounded cylinder

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  • This paper investigates the positive solutions for second order linear elliptic equation in unbounded cylinder with zero boundary condition. We prove there exist two special positive solutions with exponential growth at one end while exponential decay at the other, and all the positive solutions are linear combinations of these two.
    Mathematics Subject Classification: Primary: 35A01, 35A02; Secondary: 35A09.

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