We consider, for and , the -Laplacian evolution equation with absorption We are interested in those solutions, which we call singular solutions, that are non-negative, non-trivial, continuous in , and satisfy for all . We prove the following:
(i) When , there does not exist any such singular solution.
(ii) When , there exists, for every , a unique singular solution that satisfies as .
Also, as , where is a singular solution that satisfies as .
Furthermore, any singular solution is either or for some finite positive .
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