Browsing by Author "Kalhorn, Rebecca Isabel Burton"

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    On the Solvability of Nonlinear Boundary Value Problems on Time Scales
    (2009-04-27) Kalhorn, Rebecca Isabel Burton; James Selgrade, Committee Member; Ernest Stitzinger, Committee Member; Jesus Rodriguez, Committee Chair; Kailash Misra, Committee Member
    In this manuscript we study boundary value problems on time scales. First we will examine weakly nonlinear boundary value problems and analyze problems at resonance; that is, problems where the homogeneous linear boundary value problem has a nontrivial solution space. We establish conditions for the existence of solutions and discuss the dependence of solutions on parameters. Next we consider the existence and properties of solutions to nonlinear dynamic equations of the subject to global boundary conditions. Our most significant result in this section concerns the existence of solutions of problems where the nonlinearity exhibits sublinear growth. Finally we establish sufficient conditions for the solvability of nonlinear scalar two-point boundary value problems at resonance. As a consequence of our results we are able to provide easily verifiable conditions for the existence of periodic behavior for dynamic equations on time scales.