Abstract
The Cauchy problem for semilinear heat equations with singular initial data is studied, where N≥2, λ>0 is a parameter, and a≥0, a≠0. We show that when p>(N+2)/N and (N−2)p<N+2, there exists a positive constant such that the problem has two positive self-similar solutions and with if and no positive self-similar solutions if . Furthermore, for each fixed and in L∞(RN) as λ→0, where w0 is a non-unique solution to the problem with zero initial data, which is constructed by Haraux and Weissler.
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