Positive solutions to elliptic equations in unbounded cylinder

Jun  Bao; Lihe  Wang; Chunqin  Zhou

doi:10.3934/dcdsb.2016001

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2016, Volume 21, Issue 5: 1389-1400. Doi: 10.3934/dcdsb.2016001

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Positive solutions to elliptic equations in unbounded cylinder

1.
School of Mathematics and Information Science, Shanghai Lixin University of Commerce, Shanghai, 201620
2.
Department of Mathematics, and MOE-LSC, Shanghai Jiaotong University, Shanghai 200240

Received: April 2014

Revised: August 2015

Published: July 2016

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Abstract

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.

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Mathematics Subject Classification: Primary: 35A01, 35A02; Secondary: 35A09.

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