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Open Access Research

Oscillating global continua of positive solutions of second order Neumann problem with a set-valued term

Dongming Yan

Author Affiliations

Department of Mathematics, Sichuan University, Chengdu 610064, China

Boundary Value Problems 2012, 2012:47  doi:10.1186/1687-2770-2012-47

Published: 23 April 2012

Abstract

In this note, we study the oscillating global continua of the differential inclusion of the form

<a onClick="popup('http://www.boundaryvalueproblems.com/content/2012/1/47/mathml/M1','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2012/1/47/mathml/M1">View MathML</a>

where F is a "set-valued representation" of a function with jump discontinuities along the line segment [0, 1] × {0}, and λ ∈ [0, ∞) is a parameter. The proof of our main result relies on an approximation procedure.

Mathematics Subject Classification 2000: 34B16; 34B18.

Keywords:
climate model; differential inclusion; eigenvalue; positive solutions