EXISTENCE OF NONZERO POSITIVE SOLUTIONS OF SYSTEMS OF SECOND ORDER ELLIPTIC BOUNDARY VALUE PROBLEMS

Kunquan Lan

doi:10.11948/2011003

2011 Volume 1 Issue 1

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Kunquan Lan. EXISTENCE OF NONZERO POSITIVE SOLUTIONS OF SYSTEMS OF SECOND ORDER ELLIPTIC BOUNDARY VALUE PROBLEMS[J]. Journal of Applied Analysis & Computation, 2011, 1(1): 21-31. doi: 10.11948/2011003

Citation:

Kunquan Lan. EXISTENCE OF NONZERO POSITIVE SOLUTIONS OF SYSTEMS OF SECOND ORDER ELLIPTIC BOUNDARY VALUE PROBLEMS[J]. Journal of Applied Analysis & Computation, 2011, 1(1): 21-31. doi: 10.11948/2011003

EXISTENCE OF NONZERO POSITIVE SOLUTIONS OF SYSTEMS OF SECOND ORDER ELLIPTIC BOUNDARY VALUE PROBLEMS

Kunquan Lan

Department of Mathematics, Ryerson University Toronto, Ontario, Canada M5B 2K3

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Abstract

Abstract

Existence of nonzero positive solutions of systems of second order elliptic boundary value problems under sublinear conditions is obtained. The methodology is to establish a new result on existence of nonzero positive solutions of a flxed point equation in real Banach spaces by using the wellknown theory of flxed point index for compact maps deflned on cones, where the flxed point equation involves composition of a compact linear operator and a continuous nonlinear map. The conditions imposed on the nonlinear maps involve the spectral radii of the compact linear operators. Moreover, the nonlinear maps are not required to be increasing in ordered Banach spaces.
- Systems of elliptic boundary value problems /
- flxed point equations /
- flxed point index
MSC: 35J55

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