Lami Dozo, E.; Godoy, T.; Paczka, S. On the antimaximum principle for parabolic periodic problems with weight. (English) Zbl 1098.35069 Rend. Semin. Mat., Torino 60, No. 1, 33-44 (2002). It is proved that an antimaximum principle (AMP) holds for the Dirichlet and Neumann parabolic linear problems of second order of the type \(Lu=\lambda mu+h\) in \(\Omega \times \mathbb R\), where \(\Omega \subset \mathbb R^{N}\) is a bounded domain, the coefficients of \(L\) are sufficiently smooth functions, \(\tau\)-periodic in \(t\), the weight function \(m(x,t)\) is \(\tau\)-periodic in \(t\) and bounded, \(h(x,t)\) is \(\tau\)-periodic in \(t\) and \(h\in L^{p}(\Omega \times (0,\tau ))\) for some \(p>N+2.\) Depending on \(m\), it can be proved that in some cases the AMP holds left and right of \(\lambda^\star\), where \(\lambda^\star\) is the principal eigenvalue of the previous problem (i.e. for \(\lambda = \lambda^\star\) and \(h \equiv 0\) the problem has a positive solution). Reviewer: Luis Alberto Fernandez (Santander) Cited in 1 Document MSC: 35K20 Initial-boundary value problems for second-order parabolic equations 35P05 General topics in linear spectral theory for PDEs 47N20 Applications of operator theory to differential and integral equations 35B50 Maximum principles in context of PDEs Keywords:Dirichlet problem; Neumann problem PDFBibTeX XMLCite \textit{E. Lami Dozo} et al., Rend. Semin. Mat., Torino 60, No. 1, 33--44 (2002; Zbl 1098.35069) Full Text: EuDML