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Full-Text Articles in Mathematics
Higher Order Dynamic Equations On Measure Chains: Wronskians, Disconjugacy, And Interpolating Families Of Functions, Martin Bohner, Paul Eloe
Higher Order Dynamic Equations On Measure Chains: Wronskians, Disconjugacy, And Interpolating Families Of Functions, Martin Bohner, Paul Eloe
Paul W. Eloe
This paper introduces generalized zeros and hence disconjugacy of nth order linear dynamic equations, which cover simultaneously as special cases (among others) both differential equations and difference equations. We also define Markov, Fekete, and Descartes interpolating systems of functions. The main result of this paper states that disconjugacy is equivalent to the existence of any of the above interpolating systems of solutions and that it is also equivalent to a certain factorization representation of the operator. The results in this paper unify the corresponding theories of disconjugacy for nth order linear ordinary differential equations and for nth order linear difference …
Bifurcations In Steady State Solutions Of A Class Of Nonlinear Dispersive Wave Equation, Paul Eloe, Muhammad Usman
Bifurcations In Steady State Solutions Of A Class Of Nonlinear Dispersive Wave Equation, Paul Eloe, Muhammad Usman
Paul W. Eloe
We consider the damped externally excited KdV and BBM equations and use an asymptotic perturbation method to analyze the stability of solutions. We consider the primary resonance by defining the detuning parameter. External-excitation and frequency-response curves are shown to exhibit jump and hysteresis phenomena (dis-continuous transitions between two stable solutions) for both KdV and BBM equations.
Fully Nonlinear Boundary Value Problems With Impulse, Paul Eloe, Muhammad Usman
Fully Nonlinear Boundary Value Problems With Impulse, Paul Eloe, Muhammad Usman
Paul W. Eloe
An impulsive boundary value problem with nonlinear boundary conditions for a second order ordinary differential equation is studied. In particular, sufficient conditions are provided so that a compression- expansion cone theoretic fixed point theorem can be applied to imply the existence of positive solutions. The nonlinear forcing term is assumed to satisfy usual sublinear or superlinear growth as t → ∞ or t → 0 +. The nonlinear impulse terms and the nonlinear boundary terms are assumed to satisfy the analogous asymptotic behavior.