Singular solutions of semilinear elliptic equations with exponential nonlinearities in 2-dimensions
arxiv(2024)
摘要
By introducing a new classification of the growth rate of exponential
functions, singular solutions for semilinear elliptic equations in 2-dimensions
with exponential nonlinearities are constructed. The strategy is to introduce a
model nonlinearity which admits an explicit singular solution. Then, using a
transformation as in [8], one obtains an approximate singular solution, and
then one concludes by a suitable fixed point argument. Our method covers a wide
class of nonlinearities in a unified way. As a special case, our result
contains a pioneering contribution by Ibrahim–Kikuchi–Nakanishi–Wei [15] for
the Moser–Trudinger type nonlinearity.
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