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Upper and lower solutions and topological degree. (English) Zbl 1086.34017
Summary: 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.

MSC:
34B15Nonlinear boundary value problems for ODE
47H11Degree theory (nonlinear operators)
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References:
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