Dr. V.F. Payne-Current Research

Current (Research) Projects/Activities

  1. Investigation of the behaviour of eventually positive solutions of the equation      _u + f(u) = 0. The motivation for this study is in the behaviour for this study is in the behaviour of several mechanical systems.
  2. Extension of Sturmican Comparison principles to the general class of systems of evolution equations of parabolic and hyperbolic types with or without delays.They arise in the study of harvest, population growth and many ecological problems.
  3. The study of the asymptotic behaviour of solutions of nonlinear dynamic elasticity via energy principles.
  4. Investigation of asymptotic stability and differentiability of solutions of integrodifferential equations of visco-elasticity via dual technique oflimiting equation” result and semi-group theory.
  5. Development of numerical algorithms, generalization of results and application of techniques used in the analysis of other non-linear equations earlier studied.
  6. The study of a nonlinear integral equation via fixed point theorem of Krasnoselskii.The problem is a model of vehicular traffic and certain economic principles.
  7. Investigation of a discretization technique for decoupling systems of partial differential equations which arise in quantum mechanics.
  8. Study of properties of the eigenvalues of a 4th order singular boundary value problem.
  9. Investigation of the boundedness and stability of solutions of a system of impulsive hyperbolic differential equations with delays.
  10. The study of the global attractivity and asymptotic stability of solutions of a nonlinear equation of dynamic elasticity.
  11. The investigation of the solutions of a nonlinear problem of population dynamics using semi-group approach.