Extremal solutions and Green's functions of higher order periodic boundary value problems in time scales.

DOI10.1016/j.jmaa.2003.08.018zbMath1056.39018OpenAlexW2033633502MaRDI QIDQ1426978

Alberto Cabada

Publication date: 14 March 2004

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2003.08.018

zbMATH Keywords

Green's functiontime scalesextremal solutionsperiodic boundary value problemsMonotone iterative techniqueMaximum principlesLower and upper solutions

Mathematics Subject Classification ID

Nonlinear boundary value problems for ordinary differential equations (34B15) Time-scale analysis and singular perturbations in control/observation systems (93C70) Green's functions for ordinary differential equations (34B27) Discrete version of topics in analysis (39A12)

Related Items (23)

Existence of solutions to nonlinear first-order PBVPs on time scales ⋮ Periodicity on isolated time scales ⋮ Positive solutions for nonlinear first-order \(m\)-point boundary value problem on time scales ⋮ Monotone iterative technique for first-order nonlinear periodic boundary value problems on time scales ⋮ First-order boundary value problem with nonlinear boundary condition on time scales ⋮ Existence of positive periodic solutions for higher-order ordinary differential equations ⋮ Multiple solutions of boundary value problems on time scales for a φ-Laplacian operator ⋮ Existence of weak solutions of two-point boundary value problems for second-order dynamic equations on time scales ⋮ Existence and uniqueness results for nonlinear first-order three-point boundary value problems on time scales ⋮ Existence and multiplicity of positive solutions to nonlinear first-order PBVPs on time scales ⋮ Existence results for \(\varphi \)-Laplacian boundary value problems on time scales ⋮ On lower and upper solutions without ordering on time scales ⋮ Twin positive solutions of nonlinear first-order boundary value problems on time scales ⋮ \(I_\Delta\) and \(I^*_\Delta \)-convergence on time scales ⋮ Monotone iterative method for differential systems with coupled integral boundary value problems ⋮ Existence and nonexistence of positive solutions for second-order time scale systems ⋮ Expression of the Lebesgue \(\Delta\)-integral on time scales as a usual Lebesgue integral; application to the calculus of \(\Delta\)-antiderivatives ⋮ Nonlinear two-point boundary value problems on time scales ⋮ Positive solutions for system of first-order dynamic equations ⋮ On variational methods for periodic discrete problems ⋮ Positive solutions for nonlinear first-order periodic boundary value problems of impulsive dynamic equations on time scales ⋮ Positive solutions to nonlinear first-order PBVPs with parameter on time scales ⋮ Existence of weak solutions for second-order boundary value problem of impulsive dynamic equations on time scales

Cites Work

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• Monotone methods for a discrete boundary problem
• Remarks on the lower and upper solutions method for second- and third- order periodic boundary value problems
• The method of lower and upper solutions for \(n\)th-order periodic boundary value problems
• Optimal existence results for \(n\)th order periodic boundary value difference equations
• Second-order periodic boundary value problems on time scales
• An introduction to nonlinear boundary value problems
• Coupled solutions and monotone iterative techniques for some nonlinear initial value problems on time scales.
• Comparison results for \(n\)-th order periodic difference equations.
• Upper and lower solutions method for higher order discrete boundary value problems
• Maximum principles for fourth and sixth order periodic boundary value problems

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