Applications of a one-dimensional Sobolev inequality to eigenvalue problems

zbMath0842.34083MaRDI QIDQ1909694

Štefan Schwabik, Richard C. Brown, Don B. Hinton

Publication date: 28 July 1996

Published in: Differential and Integral Equations (Search for Journal in Brave)

zbMATH Keywords

gapsnumber of eigenvaluesPrüfer transformationone-dimensional Sobolev type inequalitySturm-Liouville boundary eigenvalue problemsupper and lower bounds for the eigenvalues

Mathematics Subject Classification ID

General spectral theory of ordinary differential operators (34L05) Inequalities for sums, series and integrals (26D15) Inequalities involving derivatives and differential and integral operators (26D10) Other analytical inequalities (26D20) Eigenvalues, estimation of eigenvalues, upper and lower bounds of ordinary differential operators (34L15)

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Positive eigenvalues of second order boundary value problems and a theorem of M. G. Krein ⋮ Existence and regularity of weak periodic solutions of the 2-D wave equation ⋮ Periodic solutions to one-dimensional wave equation with \(x\)-dependent coefficients ⋮ An upper bound for the distance between a zero and a critical point of a solution of a second order linear differential equation ⋮ An application of Sobolev's inequality to one-dimensional Kirchhoff equations ⋮ Periodic solutions to nonlinear one dimensional wave equation with 𝑋-dependent coefficients ⋮ Approximate stabilization of one-dimensional Schrödinger equations in inhomogeneous media ⋮ Time periodic solutions to a nonlinear wave equation with \(x\)-dependent coefficients ⋮ On De La Vallée Poussin-type inequalities in higher dimension and applications ⋮ Optimal control of nonlinear one-dimensional periodic wave equation with \(x\)-dependent coefficients

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