Abstract
AbstractA positive radial singular solution for $$\Delta u+f(u)=0$$
Δ
u
+
f
(
u
)
=
0
with a general supercritical growth is constructed. An exact asymptotic expansion as well as its uniqueness in the space of radial functions are also established. These results can be applied to the bifurcation problem $$\Delta u+\lambda f(u)=0$$
Δ
u
+
λ
f
(
u
)
=
0
on a ball. Our method can treat a wide class of nonlinearities in a unified way, e.g., $$u^p\log u$$
u
p
log
u
, $$\exp (u^p)$$
exp
(
u
p
)
and $$\exp (\cdots \exp (u)\cdots )$$
exp
(
⋯
exp
(
u
)
⋯
)
as well as $$u^p$$
u
p
and $$e^u$$
e
u
. Main technical tools are intrinsic transformations for semilinear elliptic equations and ODE techniques.
Funder
Japan Society for the Promotion of Science
Research Institute for Mathematical Sciences
Publisher
Springer Science and Business Media LLC
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