Maximum and anti-maximum principles for the general operator of second order with variable coefficients

This paper is devoted to the study of existence of solutions of the nonlinear second-order differential equation u ″( t)+ p( t) u ′( t)+ f( t, u( t))=0 together with different types of linear boundary conditions. To this end we assume the existence of a pair of ordered lower and upper solutions and...

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Bibliographic Details
Published in:Applied mathematics and computation 2003-01, Vol.134 (1), p.173-184
Main Authors: Barteneva, Irina V., Cabada, Alberto, Ignatyev, Alexander O.
Format: Article
Language:English
Subjects:
Comparison results
Exact sciences and technology
Lower and upper solutions
Mathematical analysis
Mathematics
Maximum principles
Nonlinear boundary value problems
Operator theory
Ordinary differential equations
Sciences and techniques of general use
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Summary:This paper is devoted to the study of existence of solutions of the nonlinear second-order differential equation u ″( t)+ p( t) u ′( t)+ f( t, u( t))=0 together with different types of linear boundary conditions. To this end we assume the existence of a pair of ordered lower and upper solutions and deduce comparison results for the general linear operator L( p, q) u( t)≡ u ″( t)+ p( t) u ′( t)+ q( t) u( t) together with the condisered boundary conditions.
ISSN:0096-3003
1873-5649
DOI:10.1016/S0096-3003(01)00280-6