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Fundamental global similarity solutions of the tenth-order thin film equation ut=∇.(|u|n∇Δ4u) in RN ×+, where n > 0 are studied. The main approach consists in passing to the limit n→0+ by using Hermitian non-self-adjoint spectral theory corresponding to the rescaled linear poly-harmonic equation ut =Δ5ut in RN ×R+

The Cauchy Problem for a Tenth-Order Thin Film Equation I. Bifurcation of Oscillatory Fundamental Solutions