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POSITIVE SOLUTIONS OF A SECOND-ORDER NEUMANN BOUNDARY VALUE PROBLEM WITH A PARAMETER

Part of: Boundary value problems

Published online by Cambridge University Press:  16 March 2012

YANG-WEN ZHANG  and
HONG-XU LI
YANG-WEN ZHANG
Affiliation:
Department of Mathematics, Sichuan University, Chengdu, Sichuan 610064, PR China (email: [email protected])
HONG-XU LI*
Affiliation:
Department of Mathematics, Sichuan University, Chengdu, Sichuan 610064, PR China (email: [email protected])
*
✉For correspondence; e-mail: [email protected]
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Abstract

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In this paper, we consider the Neumann boundary value problem with a parameter λ∈(0,∞): By using fixed point theorems in a cone, we obtain some existence, multiplicity and nonexistence results for positive solutions in terms of different values of λ. We also prove an existence and uniqueness theorem and show the continuous dependence of solutions on the parameter λ.

Keywords

dependence of parameterNeumann boundary value problempositive solutionfixed point theorem

MSC classification

Secondary: 34B18: Positive solutions of nonlinear boundary value problems
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 86 , Issue 2 , October 2012 , pp. 244 - 253
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2012

Footnotes

This work is supported by the NNSF of China (Grant No. 11071042).

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