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

@article{Barteneva2003MaximumAA,
  title={Maximum and anti-maximum principles for the general operator of second order with variable coefficients},
  author={Irina V. Barteneva and Alberto Cabada and Alexander O. Ignatyev},
  journal={Applied Mathematics and Computation},
  year={2003},
  volume={134},
  pages={173-184}
}
This paper is devoted to the study of existence of solutions of the nonlinear secondorder differential equation u00ðtÞ þ pðtÞu0ðtÞ þ f ðt; uðtÞÞ 1⁄4 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 Lðp; qÞuðtÞ u00ðtÞ þ pðtÞu0ðtÞ þ qðtÞuðtÞ together with the condisered boundary conditions. 2002 Elsevier Science Inc. All rights reserved.