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Open problems: Applying non-self-adjoint operator techniques to the \(p\)-Laplace non-linear operator in one dimension. (English) Zbl 1260.47088

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.)
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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
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