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Summary form only given. A theory is developed of ion-acoustic resonances in an inhomogeneous plasma diode using a fluid plasma description. A 1D non-linear steady state model is first developed, to which linear perturbations are applied. Poisson's equation is included self-consistently, with out making the assumption of quasineutrality. The resulting fifth order differential equation describing the wave does not have the singularity that occurs in the sheath region when quasineutrality is assumed. It is shown that both even and odd ion-acoustic resonances are confined within the plasma core. To numerically investigate long time scale, low frequency phenomena, a hybrid electrostatic PIC algorithm is used in which the electrons reach thermodynamic equilibrium with the ions each time step, using the nonlinear Boltzmann relationship for the electrons with a PIC ion source term. The 1D non-linear steady state model is compared to the PIC simulations. Also, the mode structure of the ion-acoustic resonances are compared with the pure fluid model as well as using the steady state hybrid PIC spatial profiles, n/sub e/(x), n/sub i/(x), and u/sub i/(x), as the source for the linear made analysis.