Abstract
In this chapter we recall some results in Cabada and Tojo (GJMS, 2(1), 1–8, 2013, [1], Bound. Value Probl. 2014(1), 99, 2014, [2], Nonlinear Anal. 78, 32–46, 2013, [3]). We start studying the first order operator \(x'(t)\,+\,m\,x(-t)\) coupled with periodic boundary value conditions. We describe the eigenvalues of the operator and obtain the expression of its related Green’s function in the nonresonant case. We also obtain the range of the values of the real parameter m for which the integral kernel, which provides the unique solution, has constant sign. In this way, we automatically establish maximum and anti-maximum principles for the equation.
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- 1.
\(a\,b>0\) is equivalent to \(|b-a|<|b+a|\) if \(a^2<b^2\).
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Cabada, A., Tojo, F.A.F. (2015). Order One Problems with Constant Coefficients. In: Differential Equations with Involutions. Atlantis Briefs in Differential Equations. Atlantis Press, Paris. https://doi.org/10.2991/978-94-6239-121-5_3
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DOI: https://doi.org/10.2991/978-94-6239-121-5_3
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