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

Published online by Cambridge University Press:  16 March 2012

YANG-WEN ZHANG
Affiliation:
Department of Mathematics, Sichuan University, Chengdu, Sichuan 610064, PR China (email: zhangyan_569088080@qq.com)
HONG-XU LI*
Affiliation:
Department of Mathematics, Sichuan University, Chengdu, Sichuan 610064, PR China (email: hoxuli@sohu.com)
*
For correspondence; e-mail: hoxuli@sohu.com
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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.

Type
Research Article
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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