Boulton, Lyonell Open problems: Applying non-self-adjoint operator techniques to the \(p\)-Laplace non-linear operator in one dimension. (English) Zbl 1260.47088 Integral Equations Oper. Theory 74, No. 1, 1-2 (2012). Summary: A list of open problems involving the \( q \)-sine functions is proposed. An emphasis is made on their basis properties and their ability to capture regularity of periodic functions. MSC: 47N20 Applications of operator theory to differential and integral equations 00A07 Problem books 34B15 Nonlinear boundary value problems for ordinary differential equations 34L10 Eigenfunctions, eigenfunction expansions, completeness of eigenfunctions of ordinary differential operators 34L40 Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) Keywords:eigenfunctions of \(p\)-Laplacian; basis properties of \(q\)-sine functions; regularity properties of \(q\)-sine functions PDFBibTeX XMLCite \textit{L. Boulton}, Integral Equations Oper. Theory 74, No. 1, 1--2 (2012; Zbl 1260.47088) Full Text: DOI References: [1] Binding P., Boulton L., Drábek P., Cepicka J., Girg P.: Basis properties of eigenfunctions of the p-Laplacian. Proc. AMS. 134, 3487–3494 (2006) · Zbl 1119.34064 · doi:10.1090/S0002-9939-06-08001-4 [2] Boulton L., Lord G.: Approximation properties of the q-sine bases. Proc. R. Soc. A 467, 2690–2711 (2011) · Zbl 1251.35058 · doi:10.1098/rspa.2010.0486 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.