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Upper and Lower Solutions and Topological Degree

✍ Scribed by Irena Rachůnková

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
533 KB
Volume
234
Category
Article
ISSN
0022-247X

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✦ Synopsis

This paper deals with second order nonlinear boundary value problems. We suppose the existence of upper and lower solutions of the problems which are well ordered, i.e., the lower solution is less than the upper one, and we also consider the case of upper and lower solutions having the opposite ordering. We prove the relation between the topological degree and strict upper and lower solutions in both cases and using this we get the existence and multiplicity results for the boundary value problems under consideration.

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✍ Donal O'Regan; Ravi P Agarwal 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 159 KB

This paper presents an upper and lower solution theory for singular boundary value problems where the nonlinearity may be singular in the dependent variable. In addition our nonlinearity is allowed to change sign.