We investigate existence, uniqueness and positivity of minimizers or critical points for an energy functional which contains only p-homogeneous and linear terms, 1<p<∞. Nonlinear spectral methods are used to find necessary and sufficient conditions for the existence of a minimizer. These methods are then combined with the pointwise order relation in a Sobolev space to obtain positivity and uniqueness of minimizers or critical points. A crucial restriction on the p-homogeneous part of the energy functional is that it be given by the p-th power of an equivalent, uniformly convex norm on the underlying Sobolev space. Finally, continuous dependence of minimizers on the energy functional is established.
Positivity – Springer Journals
Published: Oct 12, 2004
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